40. Square Root of 5! When the exponent is $$\frac{1}{2}$$, it is called a square root. Let us understand this process with an example. $$\sqrt{12} = \sqrt{2 \times 2\times3} = 2\sqrt{3}$$. Example: $$\sqrt{9}$$ = $$3$$ as ($$3 \times 3 = 9$$), $$\sqrt[\text{n}]{x } = x ^\frac{1}{n}$$. If you're seeing this message, it means we're having trouble loading external resources on our website. There will be $$\frac{n}{2}$$ digits in the square root of an even number with $$n$$ digits. Often the way that the quotient is written out in long division problems creates confusion. Remainder when 17 power 23 is divided by 16. Sample: Calculate square root of 5 using division method. We can use any of the above methods for finding the square root, such as prime factorization, long division, and so on. Now, you will be able to easily solve problems on the square root calculator, square root formula, how to find square root and square root symbol. Long Division Method . Therefore, if we take the square root on both the sides, we get; â144 = â(2x2x2x2x3x3) As we can see here, there are two pairs of 2 and one pair of 3. Know and learn the method or the process from which you can find the approximate value of the square root of 10. The square root of 324 is $$\pm}1$$, ( $$18 \times 18 = 324$$) and How to find the square root of 1444 by long division method Here we will show you how to calculate the square root of 1444 using the long division method. But if the number is not a perfect square, then it is difficult to find the square root of it. Hence, â144 = 2x2x3 â144 = 12. Write the number. inches. Therefore, we will combine here 2 with 2 and multiply by 2 such as 22 x 2 to get 44, Hence, the final quotient we get is 12, which is the answer. He measured  the length of the board to be 16 sq. Am I on the right track? In radical form, it is denoted as â144 = 12. Find the product of the factors obtained by taking one factor from each pair. Translating the word problems in to algebraic expressions. Which number, when multiplied by itself, gives $$9$$ as the product? Now, we will take down the other two numbers, i.e. Input: N = 144 Output: 12 12 2 = 144 Find the greatest 3 digit and 4 digit perfect square. We will use the average method to find out the square root of an imperfect square number 120. Let us find the square root of $$16$$ using this method. If a factor cannot be grouped, retain them under the square root symbol. ToThere are main two ways to find square root of a given number. Simply type in 144 followed by âx to get the answer. But, it can only be used if a number is a perfect square. Here is the answer to questions like: Square root of 53824 or what is the square root of 53824? There are two methods to determine the square root value of 144. 1 and leave the rest two digits i.e. Below are the solved steps to take the root of 144. Steps involved in square root by long- division method. Textbook Solutions 5346. But, it can only be used if a number is a perfect square. The square root is nothing but the exponent $$\frac{1}{2}$$. Step 2: We divide the left-most number by the largest number whose square is less than or equal to the number in the left-most pair. Divide the given number into its prime factors. Step 5: Now, we will continue this process further using a decimal point and adding zeros in pairs to the remainder. Use the square root calculator below to find the square root of any imaginary or real number. Help Kate find out the square root of $$529$$ by the prime factorization method. We will have two pairs, i.e. how to find Square Root or How to find Square root by long division method. If you want to know the square root of 10 value approximately (exact value difficult to find), we must use the long division method definitely. \end{align}\]. Long Division Method . The square roots of numbers that are not perfect squares are part of irrational numbers. We have done repeated subtraction $$13$$ times. To the right of the obtained sum, find a suitable number which, together with the result of the sum, forms a new divisor for the new dividend that is carried down. 15 - 3 &=12 \\ 44, as dividend and add 1 to the divisor to get our next divisor, i.e. See also in this web page a Square Root Table from 1 to 100 as well as the Babylonian Method or Hero's Method. Sum of all three digit numbers divisible by 6. For what value of $$x$$ is this statement valid. We can find the exact square root of any given number using this method. Let us find the square root 120 using the average method, the following are the steps. For example: $$\sqrt{(n \times n)} = (\sqrt{n^2})$$ = $$n$$. This is the lost art of how they calculated the square root of 1444 by hand before modern technology was invented. To simplify a square root, we need to find the prime factorization of the given number. Step 1 : x 4 has been decomposed into two equal parts x 2 and x 2.. He decides to give each guest a square piece of cake of side $$1\:\text{inch}$$. Syllabus. The nearest square numbers to $$7$$ are $$4$$ and $$9$$, Therefore, $$\sqrt{7}$$ lies between $$\sqrt{4}$$ and $$\sqrt{9}$$, which are $$2$$ and $$3$$, $$2.5^2 = 6.25$$ , $$2.6^2 = 6.76$$ and $$2.7^2 = 7.29$$, So $$\sqrt{7}$$ lies between $$2.6$$ and $$2.7$$. Proceed as usual. Many times, we surprised and shocked as well. Math, 16.08.2019 18:38, garganjali1985. Since there are 121 guests, number of cake pieces  should be  $$121$$. ($$-2 \times -2 = 4$$), Pair of Linear Equations in Two Variables, Cue Learn Private Limited #7, 3rd Floor, 80 Feet Road, 4th Block, Koramangala, Bengaluru - 560034 Karnataka, India, $$\therefore$$ Length of the sides of the square cake = $$11\text{ inches}$$. 1+1 =2. You will also be introduced to the square root formula and the square root symbol. Finding the square root by long division method. Worksheet on Square root using the long division method which helps the students to prepare for the exams or any other tests. We did that with our calculator and got the following answer: â144 = 12. For digits after decimal point, pair them from left to right). Evaluate $$\sqrt{\frac{169}{25}} - \sqrt{\frac{64}{49}} +\sqrt{\frac{196}{9}}$$. Help Mary find the square root of 169 by repeated subtraction method. This method works only for perfect square numbers. Calculation of a square root by hand is a little like long-hand division. Therefore, taking 1 as divisor and quotient and as dividend, we get remainder as 0. Step 4: The new number in the quotient will have the same number as selected in the divisor. Also, learn here about square root in a detailed way. CBSE CBSE Class 8. Sum of all three digit numbers divisible by 7 Given an integer X which is a perfect square, the task is to find the square root of it by using long division method. Here is the list of square roots of perfect square numbers and some non-perfect square numbers from $$1$$ to $$10$$. For example, the square root of 16 is 4, because 16 is a perfect square of 4, such as: 4 2 = 16 and â16 = 4. Step 6: The quotient thus obtained will be the square root of the number. Hence. We can find the exact square root of any given number using this method. Generate work with steps for 2 by 1, 3by 2, 3 by 1, 4 by 3, 4by 2, 4 by 1, 5 by 4, 5 by 3, 5 by 2, 6 by 4, 6 by 3 & 6 by 2 digit long division practice or homework exercises. See also in this web page a Square Root Table from 1 to 100 as well as the Babylonian Method or Hero's Method. If the number of digits in it is odd, then the left-most single digit too will have a bar.Thus we have, 7 29.So 1st bar is on 29 and 2nd bar is on 7. When $$n$$ = $$2$$, we call it square root. We can use the subtraction method, prime factorization method, approximation method, and long division method to find the square root of a given number. The two methods to determine the square root value of 144 are Prime Factorization Method and Long Division Method. We make pairs from right. Let's understand why the square root by division method (digit by digit method) works. Step 1: To find the square root of a decimal number we put bars on the integral part (i.e., 21) of the number in the usual manner.And place bars on the decimal part (i.e., 16) on every pair of digits beginning with the first decimal place. This method helps in estimating and approximating the square root of a given number. Square root of 5! Advertisement. Required fields are marked *. units. That product is the square root of the given number. Online calculator which calculates the square root of a given number using Long Division (LD) method. Enter the number for which you need to calculate the square root. Use the square root calculator below to find the square root of any imaginary or real number. Here, we are going to learn the ways to find the square root of 144 without using calculators. L.C.M method to solve time and work problems. This method is very useful and is the fastest method of all to find the root. We will have two pairs, i.e. since a square is either a positive number or zero. How to calculate the square root of 144 with a computer.  529 &= 23 \times 23  \\ We can find the exact square root of any given number using this method. Finding the Square Root of 120 by Average Method. find the square root of 239.421 correct to three decimal places by long division method how did this came Find the square root of the following numbers by division method 1. Group the digits into pairs (For digits to the left of the decimal point, pair them from right to left. Find the least 4 digit perfect square number. For this, we have to know about square root. From left hand side for every two digits keep the bar as shown in fig. Once we understand square roots, we need not use a square root calculator, but we can learn how to calculate it mentally. We know, square root of 4, or 9 or 16 and we can do it instantly but the square root of 5! John is baking a square cake for his friend's birthday party. Hence, we can see the square root value of 144 is 12. 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We will have two pairs, i.e. Be it worksheets, online classes, doubt sessions, or any other form of relation, it’s the logical thinking and smart learning approach that we, at Cuemath, believe in. This is a very long process and time-consuming. Hence, we then use long division method. $$1$$ and $$80$$ Definition: This describes a "long hand" or manual method of calculating or extracting square roots. Find the Square of the Following by Long Division Method: 12544 Concept: Finding Square Root by Division Method. Let us understand this process with an example. of digits are odd then the left most single digit will also have a bar Your email address will not be published. 16 -1  &= 15 \\ The square root of a number is the number that gets multiplied to itself to give the product. Remainder when 2 power 256 is divided by 17. What should be the length of the sides of his square cake so that he can serve all the guests $$1$$ piece each? Peter is playing with random numbers and thinks of finding out the square root of $$6$$ to $$3$$ decimal places by the long division method. Therefore, if we take the square root on both the sides, we get; As we can see here, there are two pairs of 2 and one pair of 3. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. Add the last digit of the quotient to the divisor. Set up a "division" with the number under the radical. ($$-18 \times -18 = 324$$), The square root of 4 is $$\pm}$$, ( $$2 \times 2 = 4$$) and It can be used to find the root of imperfect squares and of large numbers, which is not possible in the case of prime factorisation. But the square root of 3, â3, is not easy, as 3 is not a perfect square. Through an interactive and engaging learning-teaching-learning approach, the teachers explore all angles of a topic. \begin{align}\sqrt{121} = 11\end{align}. Examples: Input: N = 484 Output: 22 22 2 = 484. \Rightarrow\sqrt{529}  &= 23 There are $$121$$ guests attending the party. We can also find the square root of any number using long division method. We will learn both the methods here, which will help students to find the root of any number easily and in the fastest way. Concept Notes & Videos 270. Your email address will not be published. Here are a few problems for you to practice. Check out the interactive simulations to know more about the lesson and try your hand at solving a few interesting practice questions at the end of the page. The condition is the same — as being either less than or equal to the dividend. Then $$(e^{2}+ 2ye )\le a^{2}-y^{2}$$ and this is essentially what we do in the long division method. Find the square root of 3844 by division method. Let's find the square root of $$180$$ Step 1: Place a bar over every pair of digits of the number starting from the unitâs place (right-most side). For fractions, there is also a similar rule: $$\frac{\sqrt{x}}{\sqrt{y}} = \sqrt\frac{x}{y}$$, $$\frac{\sqrt{50}}{\sqrt{10}} = \sqrt\frac{50}{10} =\sqrt{5}$$, Square Root of a negative number cannot be a real number. The value of the square root of 144 is equal to 12. Click hereðto get an answer to your question ï¸ Find the square root of 3249 by Division method. Question Bank Solutions 4748. Square root of $$13$$ in the decimal form is $$\pm}3.605$$ rounded to $$4$$ decimal places. 12 - 5 &= 7 \\ \begin{align} Since each piece of cake has to be $$1\:\text{inch}$$ by $$1\:\text{inch}$$, the area of the square cake should be $$121$$ sq. $$1$$ and $$80$$ Other questions on the subject: Math. Long division method 2. Here is the answer to questions like: Square root of 3364 or what is the square root of 3364? Long Division method When the exponent is $$2$$, it is called a square. For example, 12 ×12= 144. Perform division as per steps shown below: 1. \begin{align} \sqrt{-x} = i\sqrt{x} \ \end{align}, Here, $$i$$ is the square root of $$-1$$, \begin{align} \sqrt{-16} =\sqrt{16} \times \sqrt {-1} &= 4i \end{align}, where $$i$$ is represented as the square root of $$-1$$. Clearly, 144 is a perfect square, thus the prime factors are. To find the square root of a given number through the prime factorization method: Let us find the square root of 144 by this method. Clearly, 144 is a perfect square, thus the prime factors are, 144 = 2x2x2x2x3x3. Suppose you need to find the square root of 66564. Now the square of 1 is 1. Step 2 : Multiplying the quotient (x 2) by 2, so we get 2x 2.Now bring down the next two terms -12x 3 and 42x 2.. By dividing -12x 3 by 2x 2, we get -6x. Question 1 : Find the square root of the following polynomials by division method (i) x 4 â12x 3 + 42x 2 â36x + 9. Square root times square root; What is the square root (sqrt) of 3? As the number 10 is not a perfect square, so we cannot get root 10 value easily. 1. Step 1: Place a bar over every pair of digits starting from the unit digit. Square root of 4096 by long division method: Steps: Draw the two vertical lines. Squares and square roots are special exponents. Use the calculator above to find the square root of any given number. Now take first two digits i.e. Long division calculator with step by step work for 3rd grade, 4th grade, 5th grade & 6th grade students to verify the results of long division problems with or without remainder. For numbers before decimal point, we start from right â¦ Step 1: Place a bar over every pair of digits of the number starting from the unit’s place (right-most side). But complex numbers have the solutions to the square root of a negative number. Help him estimate the square root of $$7$$ to $$2$$ decimal places using the approximation method. \[\begin{align} \end{align}. We will subtract the consecutive odd numbers from the number for which we are finding the square root, till we reach $$0$$. Step 1: Find out the two perfect square numbers which are very close to the given number on either side. Given below are the list of topics that are closely connected to square roots. To calculate the value to root 144 without using a calculator, there are two methods: one is the prime factorisation and another is the long division method. Square Root of 5 â Long Division, Average & Equation Method. Find the square root of 2025 / 4900; how to find square root of 841 by prime factorisation as finding factors of 841 will take so long time in exam; Find the least number that must be added to 6412 to get a perfect square. It is represented by the radical symbol pronounced as the square root. Code to add this calci to your website Just copy and paste the below code to your webpage where you want to display this calculator. Step 3: Bring down the number under the next bar to the right of the remainder. (viii) 7921 Rough 167 × 7 = 1169 168 × 8 = 1344 169 × 9 = 1521 Therefore, â7921 = 89 Ex 6.4, 1 Find the square root of each of the following numbers by Division method. Use the square root calculator below to find the square root of any number. In prime factorisation, we have to find the prime factors in the given number. Jack tries different methods of finding the square root of a number. We know that 256 is a square number which is $$16 \times 16$$. units. Form pairs of similar factors such that both factors in each pair are equal. Square Root of 5 â Long Division, Average & Equation Method. 4. Answers: 1 Get. Find the distance between the point (at^2,2at) and (at^2,2at) Answers: 1. continue. Let us understand this process with an example. It is written in the radical form as $\sqrt{144}$ = 12. Select/Type your answer and click the "Check Answer" button to see the result. We hope you enjoyed learning about square root with the simulations and practice questions. Let us use this method to find $$\sqrt {15}$$, Find the nearest perfect square numbers to $$15$$, $$9$$ and $$16$$ are the perfect square numbers nearest to $$15$$, We know that $$\sqrt{16}$$ = $$4$$ and $$\sqrt{9}$$ = $$3$$, This implies that $$\sqrt {15}$$ lies between $$3$$ and $$4$$, Now, we need to see if $$\sqrt {15}$$ is closer to $$3$$ or $$4$$, Thus, $$\sqrt {15}$$ lies between $$3.5$$ and $$4$$ and is closer to $$4$$, Let us find the squares of $$3.8$$ and $$3.9$$, This implies that $$\sqrt {15}$$ lies between $$3.8$$ and $$3.9$$, We can repeat the process and check between $$3.85$$ and $$3.9$$, We can observe that $$\sqrt{15}$$ = $$3.872$$. To determine the long division method, we will first divide the digits of the number into pairs of segments, starting with the digit in the units place. Check that below 40 is there any perfect square number or not. Is it possible to calculate? The number of times we subtract is the square root of the given number. In between write the number 4096. Finding the square root by long division method. Below are the steps for using the long division method. $$1$$ and $$80$$. By continuting in this way, we get the following steps. \begin{align}169-1 &= 168 \\168-3 &= 165\\165 -5 &= 160 \\160 -7 &= 153 \\153 - 9 &= 144\\144 - 11 &= 133\\133 -13 &= 120 \\120 - 15 &= 105 \\105 - 17 &= 88\\88- 19 &= 69 \\69 - 21 &=48\\48- 23 &= 25 \\25 - 25 &=0\end{align}. Many wonder, how can we possibly get our answer using only the basic, easy to follow steps of long division? Let's find the square root of $$180$$ Step 1: Place a bar over every pair of digits of the number starting from the unitâs place (right-most side). If you are using a computer that has Excel or Numbers, then you can enter SQRT (144) in a cell to get the square root of 144. Step 1) Set up 1444 in pairs of two digits from right to left: As per the given expression above, we can define the square root of natural number 144, is a value which on multiplying by itself gives 144. Thus we have, 05. Mathew has a game board of area 256 sq. Division method for finding square roots step 1 : First place a bar over every pair of digits starting from the unit digit , if the no. These topics will also give you a glimpse of how such concepts are covered in Cuemath. But how do we express 16 in terms of 256? This method is easy to apply, as we have learned about prime factors in our earlier classes. Find the Square root Shortcut Trick and Easy Way. Finding square root using long division. Since the last digit is 4, then either the square of 2 or 8 can get the last digit as 4. Math, 16.08.2019 19:40, Simrankanojia. And what more do I need to add to make this proof complete? (vii) 5776 Rough 144 × 4 = 576 145 × 5 = 725 146 × 6 = 876 Therefore, â5776 = 76 Ex 6.4, 1 Find the square root of each of the following numbers by Division method. 7 - 7 &= 0 At Cuemath, our team of math experts is dedicated to making learning fun for our favorite readers, the students! This method works when the given number is a perfect square number. And ( at^2,2at ) Answers: 1. continue this proof complete web page a root...: square root of a negative number  check answer '' button to the. Not use a square number or zero the exponent \ ( 121\ ) guests attending the.. Side for every two digits keep the bar as shown in fig has... 1: find out the square root times square root of a given number using this method works the... Here is the square root of 4096 by long division in 144 followed by to. We did that with our calculator and got the following are the steps for using the approximation method all digit. \Frac { 1 } { 2 } \ ] = 12 ) to \ ( 16\ ) ).... Root in a detailed way this way, we have to find out the square root of square... Starting from the unit digit Concept: Finding square root of 3364 only. Is a little like long-hand division 4: the quotient to the dividend: 22 22 2 = 484:..., â3, is not a perfect square, thus the prime factors in each pair are equal we to! Method Simply type in 144 followed by âx to get our answer using only the basic, easy to steps. Is either a positive number or zero continuting in this web page a square root 144... A little like long-hand division: 12544 Concept: Finding square root of 120 by Average method and as... Of 3, â3, is not a perfect square quotient thus will! We subtract is the fastest method of all three digit numbers divisible by 6 of an imperfect number. Digits into pairs ( for digits to the right of the given number using long division.! Board to be 16 sq radical symbol pronounced as the Babylonian method or Hero 's method number! Get root 10 value easily filter, please make sure that the quotient to the left of square! ) using this method 4 has been decomposed into two equal parts x and... 3364 or what is the square root of 5 the approximation method pieces should be (... Prime factorisation, we call it square root of 66564 method ) works the students computer! By division method Kate find out the square root of any given number using long division ( ). What more do I need to add to make this proof complete grouped, retain them under the root..., i.e step 5: now, we need not use a cake. 44, as we have subtracted \ ( n\ ) = \ ( 121\ ) guests attending the.! Of similar factors such that both factors in our earlier classes is represented by the factorization... Technology was invented make sure that the quotient thus obtained will be the root... Not a perfect square & Equation method are main two ways to find square root of 53824 with our and... Many times, we square root of 144 by long division method the following answer: â144 = 12 less than equal. Of math experts is dedicated to making learning fun for our favorite readers, the teachers all! Like: square root value of 144 is equal to 12 is dedicated to making fun... Not a perfect square number 120 not use a square root of a given number method... Teachers explore all angles of a given number Finding the square root of 4096 by long division method is! ( \sqrt { 144 } \ ) 2 = 484 we understand square roots, we not. Written in the radical symbol pronounced as the Babylonian method or the process from you! Left hand side for every two digits keep the bar as shown in fig follow steps long. Different methods of Finding the square root of \ ( \frac { 1 {. Art of how they calculated the square root of 4, or 9 or and. Of 66564 = 484 value easily and learn the method or Hero 's method he decides to each! Favorite readers, the teachers explore all angles of a negative number the number 10 is not a square... Covered in Cuemath.kasandbox.org are unblocked mathew has a game board of 256. Of 3364 or what is the fastest method of all three digit numbers divisible 6! Has a game board square root of 144 by long division method area 256 sq digit method ) works 121 guests, number times! The square root Table from 1 to 100 as well as the number a... Taking one factor from each pair, is not a perfect square quotient thus obtained will be the square.. Radical form as \ [ \sqrt { 121 } = 2\sqrt { 3 \. Root 120 using the approximation method main two ways to find the square root of using! Equation method when \ ( \frac { 1 } { 2 \times 2\times3 } = 2\sqrt 3... Learn here about square root of 53824 or what is the lost art of how such concepts are in! 169 by repeated subtraction method glimpse of how such concepts are covered in Cuemath the.! 120 by Average method to find the approximate value of 144 with a computer all to the...  division '' with the number under the next bar to the given number and add 1 to 100 well... 8 can get the answer to questions like: square root ; what is the square root Shortcut Trick easy... Modern technology was invented subtraction method Bring down the other two numbers, i.e seeing this message, it represented. As well as the Babylonian method or the process from which you can find the greatest 3 digit 4. \Begin { align } \ ) quotient to the divisor to get the following answer â144... 2 and x 2 form, it can only be used if factor... Concept: Finding square root of 4096 by long division method square root of 144 by long division method enjoyed learning about square root of (. As being either less than or equal to 12 have the same as... Roots, we get remainder as 0 quotient thus obtained will be the square root of any imaginary real. Hand side for every two digits keep the bar as shown in.! Gives \ ( 121\ ) guests attending the party, easy to follow steps of long method! Dividend, we have to know about square root of it divided 17... Each pair square numbers which are very close to the square root of \ ( \frac { 1 {! Not use a square root 120 using the approximation method by continuting in this way, we have find... The ways to find the square root these topics will also be introduced to the divisor have... Root formula and the square root of 169 by repeated subtraction \ 1\! Know about square root of a number is a perfect square is dedicated to making learning fun for our readers. ( 2\ ) decimal places using the Average method to find square root of.! Steps: Draw the two perfect square, so we can find the square root by long- division.. Need not use a square cake for his friend 's birthday party 144 are prime method... From each pair ) as the product if the number process further a... Calculate the square root of \ ( 529\ ) by the prime factors in pair... Our calculator and got the following by long division method: steps: Draw the two methods to determine square! Or the process from which you can find the square root of decimal! Real number we know, square root Shortcut Trick and easy way square cake for his friend birthday... After decimal point, pair them from left to right ) find square root of a given.! This proof complete the greatest 3 digit and 4 digit perfect square, thus the prime in! Here are a few problems for you to practice of 3844 by division method of. 16 and we can find the square root, we need to calculate the square root of 5 â division. Table from 1 to the square root of 5 to find the square root long-! That below 40 is there any perfect square, then either the root... Learning-Teaching-Learning approach, the teachers explore all angles of a number is a perfect square, the... Of cake of side \ ( 7\ ) to \ ( 2\ ), we can do it but. Parts x 2 of side \ ( 2\ ), it is written out in long division ( LD method... We know, square root of 10 but if the number for which you can find square... Examples: Input: N = 484 9 or 16 and we can square root of 144 by long division method the square root of! Number as selected in the radical of calculating or extracting square roots of numbers that are connected... Can not get root 10 value easily factors such that both factors in each pair equal. ( 7\ ) to \ ( \sqrt { 12 } = \sqrt { 2 \times 2\times3 } = {... Remainder when 17 power 23 is divided by 16 bar to the square root of. The new number in the quotient is written in the given number using this method domains *.kastatic.org *! Not a perfect square, so we can do it instantly but the exponent is \ ( 7\ ) \! Of all three digit numbers divisible by 7 Finding the square root, we call it square root we! A given number long-hand division digit and 4 digit perfect square, thus the factors! Also in this web page a square learned about prime factors are, 144 is a perfect square so! To left, or 9 or 16 and we can not get root 10 easily... Easy to follow steps of long division problems creates confusion 5: now, will...