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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 5329.</p>

4 <h2>What is the Square Root of 5329?</h2>

5 <p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 5329 is a<a>perfect square</a>. The square root of 5329 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √5329, whereas (5329)^(1/2) in the exponential form. √5329 = 73, 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 5329</h2>

7 <p>The<a>prime factorization</a>method is used for perfect square numbers. For non-perfect square numbers, the long-<a>division</a>method and approximation method are used. Since 5329 is a perfect square, let us use the prime factorization method:</p>

8 <ul><li>Prime factorization method</li>

9 <li>Long division method</li>

10 <li>Approximation method</li>

11 </ul><h2>Square Root of 5329 by Prime Factorization Method</h2>

12 <p>The<a>product</a>of prime<a>factors</a>is the Prime factorization of a number. Now let us look at how 5329 is broken down into its prime factors.</p>

13 <p><strong>Step 1:</strong>Finding the prime factors of 5329. Breaking it down, we get 73 x 73: 73^2.</p>

14 <p><strong>Step 2:</strong>Now, we found out the prime factors of 5329. Since it is a perfect square, the<a>square root</a>of 5329 can be calculated as the product of one factor from each pair, which is 73.</p>

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17 <h2>Square Root of 5329 by Long Division Method</h2>

16 <h2>Square Root of 5329 by Long Division Method</h2>

18 <p>The<a>long division</a>method is particularly used for non-perfect square numbers but can be applied to perfect squares as well. Let us now learn how to find the square root using the long division method, step by step.</p>

17 <p>The<a>long division</a>method is particularly used for non-perfect square numbers but can be applied to perfect squares as well. Let us now learn how to find the square root using the long division method, step by step.</p>

19 <p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 5329, we need to group it as 53 and 29.</p>

18 <p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 5329, we need to group it as 53 and 29.</p>

20 <p><strong>Step 2:</strong>Find a number whose square is<a>less than</a>or equal to 53. The number is 7, as 7 x 7 = 49.</p>

19 <p><strong>Step 2:</strong>Find a number whose square is<a>less than</a>or equal to 53. The number is 7, as 7 x 7 = 49.</p>

21 <p><strong>Step 3:</strong>Subtract 49 from 53, which gives a<a>remainder</a>of 4. Bring down the next pair, 29, making the new<a>dividend</a>429.</p>

20 <p><strong>Step 3:</strong>Subtract 49 from 53, which gives a<a>remainder</a>of 4. Bring down the next pair, 29, making the new<a>dividend</a>429.</p>

22 <p><strong>Step 4:</strong>Double the<a>divisor</a>(7), which gives 14, and find a digit n such that 14n x n is less than or equal to 429. The digit is 3, as 143 x 3 = 429.</p>

21 <p><strong>Step 4:</strong>Double the<a>divisor</a>(7), which gives 14, and find a digit n such that 14n x n is less than or equal to 429. The digit is 3, as 143 x 3 = 429.</p>

23 <p><strong>Step 5:</strong>Subtract 429 from 429 to get 0. So, the square root of √5329 is 73.</p>

22 <p><strong>Step 5:</strong>Subtract 429 from 429 to get 0. So, the square root of √5329 is 73.</p>

24 <h2>Square Root of 5329 by Approximation Method</h2>

23 <h2>Square Root of 5329 by Approximation Method</h2>

25 <p>The approximation method is another way to find square roots, useful for non-perfect squares. Since 5329 is a perfect square, approximation is straightforward.</p>

24 <p>The approximation method is another way to find square roots, useful for non-perfect squares. Since 5329 is a perfect square, approximation is straightforward.</p>

26 <p><strong>Step 1:</strong>Identify perfect squares closest to 5329. The number 5329 itself is a perfect square, falling exactly at 73 x 73. Thus, the square root of 5329 is precisely 73.</p>

25 <p><strong>Step 1:</strong>Identify perfect squares closest to 5329. The number 5329 itself is a perfect square, falling exactly at 73 x 73. Thus, the square root of 5329 is precisely 73.</p>

27 <h2>Common Mistakes and How to Avoid Them in the Square Root of 5329</h2>

26 <h2>Common Mistakes and How to Avoid Them in the Square Root of 5329</h2>

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

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

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29 <h3>Problem 1</h3>

30 <p>Can you help Max find the area of a square box if its side length is given as √5329?</p>

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

32 <p>The area of the square is 5329 square units.</p>

33 <h3>Explanation</h3>

34 <p>The area of the square = side^2.</p>

35 <p>The side length is given as √5329.</p>

36 <p>Area of the square = side^2 = √5329 x √5329 = 73 × 73 = 5329.</p>

37 <p>Therefore, the area of the square box is 5329 square units.</p>

38 <p>Well explained 👍</p>

39 <h3>Problem 2</h3>

40 <p>A square-shaped building measuring 5329 square feet is built; if each of the sides is √5329, what will be the square feet of half of the building?</p>

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

42 <p>2664.5 square feet</p>

43 <h3>Explanation</h3>

44 <p>We can just divide the given area by 2 as the building is square-shaped.</p>

45 <p>Dividing 5329 by 2, we get 2664.5.</p>

46 <p>So, half of the building measures 2664.5 square feet.</p>

47 <p>Well explained 👍</p>

48 <h3>Problem 3</h3>

49 <p>Calculate √5329 x 5.</p>

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

51 <p>365</p>

52 <h3>Explanation</h3>

53 <p>The first step is to find the square root of 5329, which is 73.</p>

54 <p>The second step is to multiply 73 with 5.</p>

55 <p>So, 73 x 5 = 365.</p>

56 <p>Well explained 👍</p>

57 <h3>Problem 4</h3>

58 <p>What will be the square root of (5329 + 71)?</p>

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

60 <p>The square root is 74.</p>

61 <h3>Explanation</h3>

62 <p>To find the square root, we need to find the sum of (5329 + 71). 5329 + 71 = 5400, and then √5400 is approximately 73.48, but as 5400 is not a perfect square, it approximates to 73.48.</p>

63 <p>Well explained 👍</p>

64 <h3>Problem 5</h3>

65 <p>Find the perimeter of the rectangle if its length ‘l’ is √5329 units and the width ‘w’ is 38 units.</p>

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

67 <p>The perimeter of the rectangle is 222 units.</p>

68 <h3>Explanation</h3>

69 <p>Perimeter of the rectangle = 2 × (length + width).</p>

70 <p>Perimeter = 2 × (√5329 + 38) = 2 × (73 + 38) = 2 × 111 = 222 units.</p>

71 <p>Well explained 👍</p>

72 <h2>FAQ on Square Root of 5329</h2>

73 <h3>1.What is √5329 in its simplest form?</h3>

74 <p>The prime factorization of 5329 is 73 x 73, so the simplest form of √5329 = √(73 x 73) = 73.</p>

75 <h3>2.Is 5329 a perfect square?</h3>

76 <p>Yes, 5329 is a perfect square, as it can be expressed as 73 x 73.</p>

77 <h3>3.Calculate the square of 5329.</h3>

78 <p>To find the square of 5329, we multiply the number by itself, that is 5329 x 5329 = 28,398,241.</p>

79 <h3>4.Is 5329 a prime number?</h3>

80 <p>5329 is not a<a>prime number</a>, as it has more than two factors.</p>

81 <h3>5.What is the significance of perfect squares like 5329?</h3>

82 <p>Perfect squares are significant in mathematical problems and real-world applications as they simplify calculations, especially in<a>geometry</a>and<a>algebra</a>, where square roots are needed.</p>

83 <h2>Important Glossaries for the Square Root of 5329</h2>

84 <ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: 8^2 = 64 and the inverse of the square is the square root, that is √64 = 8.</li>

85 </ul><ul><li><strong>Rational number:</strong>A rational number is a number that can be written in the form of p/q, where q is not equal to zero, and p and q are integers.</li>

86 </ul><ul><li><strong>Perfect square:</strong>A perfect square is a number that has an integer as its square root. For example, 5329 is a perfect square because √5329 = 73.</li>

87 </ul><ul><li><strong>Prime factorization:</strong>Prime factorization involves expressing a number as a product of its prime numbers. For example, 5329 = 73 x 73.</li>

88 </ul><ul><li><strong>Long division method:</strong>A technique used to find the square root of a number by dividing it into groups and using division steps to reach the answer sequentially.</li>

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

90 <p>▶</p>

91 <h2>Jaskaran Singh Saluja</h2>

92 <h3>About the Author</h3>

93 <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>

94 <h3>Fun Fact</h3>

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