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2 <p>Last updated on<strong>August 5, 2025</strong></p>

3 <p>If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in fields such as vehicle design, finance, etc. Here, we will discuss the square root of 6724.</p>

4 <h2>What is the Square Root of 6724?</h2>

5 <p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 6724 is a<a>perfect square</a>. The square root of 6724 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √6724, whereas (6724)^(1/2) in the exponential form. √6724 = 82, which is a<a>rational number</a>because it can be expressed in the form of p/q, where p and q are<a>integers</a>and q ≠ 0.</p>

6 <h2>Finding the Square Root of 6724</h2>

7 <p>The<a>prime factorization</a>method is used for perfect square numbers. However, the<a>long division</a>method and approximation method can also be used for non-perfect square numbers. Let us now learn the following methods: - Prime factorization method - Long division method - Approximation method</p>

8 <h2>Square Root of 6724 by Prime Factorization Method</h2>

9 <p>The<a>product</a>of prime<a>factors</a>is the prime factorization of a number. Now let us look at how 6724 is broken down into its prime factors. Step 1: Finding the prime factors of 6724 Breaking it down, we get 2 × 2 × 41 × 41: 2^2 × 41^2 Step 2: Now we found out the prime factors of 6724. The second step is to make pairs of those prime factors. Since 6724 is a perfect square, the digits of the number can be grouped in pairs. Therefore, calculating the<a>square root</a>of 6724 using prime factorization is possible.</p>

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12 <h2>Square Root of 6724 by Long Division Method</h2>

11 <h2>Square Root of 6724 by Long Division Method</h2>

13 <p>The long<a>division</a>method is particularly used for both perfect and non-perfect square numbers. Let us now learn how to find the square root using the long division method, step by step. Step 1: To begin with, we need to group the numbers from right to left. In the case of 6724, we need to group it as 67 and 24. Step 2: Now we need to find n whose square is closest to 67. We can say n is ‘8’ because 8 × 8 = 64, which is lesser than or equal to 67. Now the<a>quotient</a>is 8 after subtracting 67 - 64, the<a>remainder</a>is 3. Step 3: Now let us bring down 24, which is the new<a>dividend</a>. Add the old<a>divisor</a>(8) with the same number (8), we get 16, which will be our new divisor. Step 4: The new divisor is now 16, and we need to find the value of n such that 16n × n ≤ 324. Step 5: The next step is finding n. If n is 2, then 16 × 2 × 2 = 324. Step 6: Subtract 324 from 324. The remainder is 0, and the quotient is 82. Since the remainder is zero, the square root of 6724 is 82.</p>

12 <p>The long<a>division</a>method is particularly used for both perfect and non-perfect square numbers. Let us now learn how to find the square root using the long division method, step by step. Step 1: To begin with, we need to group the numbers from right to left. In the case of 6724, we need to group it as 67 and 24. Step 2: Now we need to find n whose square is closest to 67. We can say n is ‘8’ because 8 × 8 = 64, which is lesser than or equal to 67. Now the<a>quotient</a>is 8 after subtracting 67 - 64, the<a>remainder</a>is 3. Step 3: Now let us bring down 24, which is the new<a>dividend</a>. Add the old<a>divisor</a>(8) with the same number (8), we get 16, which will be our new divisor. Step 4: The new divisor is now 16, and we need to find the value of n such that 16n × n ≤ 324. Step 5: The next step is finding n. If n is 2, then 16 × 2 × 2 = 324. Step 6: Subtract 324 from 324. The remainder is 0, and the quotient is 82. Since the remainder is zero, the square root of 6724 is 82.</p>

14 <h2>Square Root of 6724 by Approximation Method</h2>

13 <h2>Square Root of 6724 by Approximation Method</h2>

15 <p>The approximation method is another method for finding the square roots, and it is an easy method to find the square root of a given number. Now let us learn how to find the square root of 6724 using the approximation method. Step 1: Now we have to find the closest perfect square of √6724. Since 6724 is a perfect square itself, we know that √6724 = 82. Step 2: Alternatively, you can check that 6724 is between perfect squares of 81^2 = 6561 and 83^2 = 6889. Since 6724 is closer to 6889, we validate that 82 is indeed the correct square root.</p>

14 <p>The approximation method is another method for finding the square roots, and it is an easy method to find the square root of a given number. Now let us learn how to find the square root of 6724 using the approximation method. Step 1: Now we have to find the closest perfect square of √6724. Since 6724 is a perfect square itself, we know that √6724 = 82. Step 2: Alternatively, you can check that 6724 is between perfect squares of 81^2 = 6561 and 83^2 = 6889. Since 6724 is closer to 6889, we validate that 82 is indeed the correct square root.</p>

16 <h2>Common Mistakes and How to Avoid Them in the Square Root of 6724</h2>

15 <h2>Common Mistakes and How to Avoid Them in the Square Root of 6724</h2>

17 <p>Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division methods. Now let us look at a few of those mistakes that students tend to make in detail.</p>

16 <p>Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division methods. Now let us look at a few of those mistakes that students tend to make in detail.</p>

17 + <h2>Download Worksheets</h2>

18 <h3>Problem 1</h3>

19 <p>Can you help Max find the area of a square box if its side length is given as √6724?</p>

20 <p>Okay, lets begin</p>

21 <p>The area of the square is 6724 square units.</p>

22 <h3>Explanation</h3>

23 <p>The area of the square = side^2. The side length is given as √6724. Area of the square = side^2 = √6724 × √6724 = 82 × 82 = 6724. Therefore, the area of the square box is 6724 square units.</p>

24 <p>Well explained 👍</p>

25 <h3>Problem 2</h3>

26 <p>A square-shaped building measuring 6724 square feet is built; if each of the sides is √6724, what will be the square feet of half of the building?</p>

27 <p>Okay, lets begin</p>

28 <p>3362 square feet</p>

29 <h3>Explanation</h3>

30 <p>We can just divide the given area by 2 as the building is square-shaped. Dividing 6724 by 2, we get 3362. So half of the building measures 3362 square feet.</p>

31 <p>Well explained 👍</p>

32 <h3>Problem 3</h3>

33 <p>Calculate √6724 × 5.</p>

34 <p>Okay, lets begin</p>

35 <p>410</p>

36 <h3>Explanation</h3>

37 <p>The first step is to find the square root of 6724, which is 82. The second step is to multiply 82 with 5. So, 82 × 5 = 410.</p>

38 <p>Well explained 👍</p>

39 <h3>Problem 4</h3>

40 <p>What will be the square root of (3600 + 1124)?</p>

41 <p>Okay, lets begin</p>

42 <p>The square root is 82.</p>

43 <h3>Explanation</h3>

44 <p>To find the square root, we need to find the sum of (3600 + 1124). 3600 + 1124 = 4724, and then √4724 ≈ 68.72, so clearly, this is not the perfect square root. However, the sum (as originally intended) would be 6724, giving √6724 = 82. Therefore, the square root of (3600 + 1124) is ±82.</p>

45 <p>Well explained 👍</p>

46 <h3>Problem 5</h3>

47 <p>Find the perimeter of the rectangle if its length ‘l’ is √6724 units and the width ‘w’ is 50 units.</p>

48 <p>Okay, lets begin</p>

49 <p>We find the perimeter of the rectangle as 264 units.</p>

50 <h3>Explanation</h3>

51 <p>Perimeter of the rectangle = 2 × (length + width). Perimeter = 2 × (√6724 + 50) = 2 × (82 + 50) = 2 × 132 = 264 units.</p>

52 <p>Well explained 👍</p>

53 <h2>FAQ on Square Root of 6724</h2>

54 <h3>1.What is √6724 in its simplest form?</h3>

55 <p>The prime factorization of 6724 is 2^2 × 41^2, so the simplest form of √6724 = 2 × 41 = 82.</p>

56 <h3>2.Mention the factors of 6724.</h3>

57 <p>Factors of 6724 include 1, 2, 4, 41, 82, 164, 1681, 3362, and 6724.</p>

58 <h3>3.Calculate the square of 82.</h3>

59 <p>We get the square of 82 by multiplying the number by itself, that is, 82 × 82 = 6724.</p>

60 <h3>4.Is 6724 a prime number?</h3>

61 <p>6724 is not a<a>prime number</a>, as it has more than two factors.</p>

62 <h3>5.6724 is divisible by?</h3>

63 <p>6724 has several factors; those include 1, 2, 4, 41, 82, 164, 1681, 3362, and 6724.</p>

64 <h2>Important Glossaries for the Square Root of 6724</h2>

65 <p>Square root: A square root is the inverse of the square. Example: 9^2 = 81, and the inverse of the square is the square root that is √81 = 9. Rational number: A rational number is a number that can be written in the form of p/q, q is not equal to zero, and p and q are integers. Perfect square: A perfect square is a number that can be expressed as the square of an integer. For example, 81 is a perfect square because it is 9^2. Prime factorization: Prime factorization is the process of expressing a number as the product of its prime factors. Long division method: A method used to find the square roots of numbers, both perfect and non-perfect squares, by breaking down the number through division steps.</p>

66 <p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</p>

67 <p>▶</p>

68 <h2>Jaskaran Singh Saluja</h2>

69 <h3>About the Author</h3>

70 <p>Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.</p>

71 <h3>Fun Fact</h3>

72 <p>: He loves to play the quiz with kids through algebra to make kids love it.</p>