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2 <p>Last updated on<strong>September 30, 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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 529.</p>

4 <h2>What is the Square Root of 529?</h2>

5 <p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 529 is a<a>perfect square</a>. The square root of 529 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √529, whereas (529)(1/2) in the exponential form. √529 = 23, 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 529</h2>

7 <p>The<a>prime factorization</a>method is used for perfect square numbers. Since 529 is a perfect square, we can use the prime factorization method. Other methods such as the<a>long division</a>method or approximation method can also be used but are not necessary in this case.</p>

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

9 <li>Long division method</li>

10 <li>Approximation method</li>

11 </ol><h2>Square Root of 529 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 529 is broken down into its prime factors.</p>

13 <p><strong>Step 1:</strong>Finding the prime factors of 529 529 = 23 × 23 = 232</p>

14 <p><strong>Step 2:</strong>Since 529 is a perfect square, we can take one number from each pair of identical factors.</p>

15 <p>The<a>square root</a>of 529 is 23.</p>

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18 <h2>Square Root of 529 by Long Division Method</h2>

17 <h2>Square Root of 529 by Long Division Method</h2>

19 <p>The long<a>division</a>method can also be used for perfect square numbers. It involves dividing the number into groups from right to left and finding the square root step by step.</p>

18 <p>The long<a>division</a>method can also be used for perfect square numbers. It involves dividing the number into groups from right to left and finding the square root step by step.</p>

20 <p><strong>Step 1:</strong>Group the digits of 529 from right to left as (5, 29).</p>

19 <p><strong>Step 1:</strong>Group the digits of 529 from right to left as (5, 29).</p>

21 <p><strong>Step 2:</strong>Find a number whose square is<a>less than</a>or equal to 5. The number is 2 because 2 × 2 = 4. Subtract 4 from 5, giving a<a>remainder</a>of 1. Bring down the next pair, 29, making it 129.</p>

20 <p><strong>Step 2:</strong>Find a number whose square is<a>less than</a>or equal to 5. The number is 2 because 2 × 2 = 4. Subtract 4 from 5, giving a<a>remainder</a>of 1. Bring down the next pair, 29, making it 129.</p>

22 <p><strong>Step 3:</strong>Double the<a>quotient</a>(2) to get 4, which will be part of our new<a>divisor</a>.</p>

21 <p><strong>Step 3:</strong>Double the<a>quotient</a>(2) to get 4, which will be part of our new<a>divisor</a>.</p>

23 <p><strong>Step 4:</strong>Find a digit (n) such that 4n × n ≤ 129. n is 3 because 43 × 3 = 129.</p>

22 <p><strong>Step 4:</strong>Find a digit (n) such that 4n × n ≤ 129. n is 3 because 43 × 3 = 129.</p>

24 <p><strong>Step 5:</strong>Subtract 129 from 129 to get a remainder of 0. The quotient is 23, so the square root of 529 is 23.</p>

23 <p><strong>Step 5:</strong>Subtract 129 from 129 to get a remainder of 0. The quotient is 23, so the square root of 529 is 23.</p>

25 <h2>Square Root of 529 by Approximation Method</h2>

24 <h2>Square Root of 529 by Approximation Method</h2>

26 <p>Since 529 is a perfect square, the approximation method isn't necessary. However, for illustration:</p>

25 <p>Since 529 is a perfect square, the approximation method isn't necessary. However, for illustration:</p>

27 <p><strong>Step 1:</strong>Identify two perfect squares between which 529 lies. Here, it is already a perfect square, i.e., 232 = 529.</p>

26 <p><strong>Step 1:</strong>Identify two perfect squares between which 529 lies. Here, it is already a perfect square, i.e., 232 = 529.</p>

28 <p><strong>Step 2:</strong>Since 529 is a perfect square, its square root is exactly 23.</p>

27 <p><strong>Step 2:</strong>Since 529 is a perfect square, its square root is exactly 23.</p>

29 <h2>Common Mistakes and How to Avoid Them in the Square Root of 529</h2>

28 <h2>Common Mistakes and How to Avoid Them in the Square Root of 529</h2>

30 <p>Students sometimes make errors while finding the square root, such as forgetting about the negative square root or making calculation mistakes. Here are a few common mistakes and how to avoid them:</p>

29 <p>Students sometimes make errors while finding the square root, such as forgetting about the negative square root or making calculation mistakes. Here are a few common mistakes and how to avoid them:</p>

30 + <h2>Download Worksheets</h2>

31 <h3>Problem 1</h3>

32 <p>What is the side length of a square with an area of 529 square units?</p>

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

34 <p>The side length of the square is 23 units.</p>

35 <h3>Explanation</h3>

36 <p>The area of the square = side2.</p>

37 <p>Given that the area is 529, we solve for the side length: side = √529 = 23.</p>

38 <p>Therefore, the side length is 23 units.</p>

39 <p>Well explained 👍</p>

40 <h3>Problem 2</h3>

41 <p>If a square-shaped tile has a side length of √529, what is the perimeter of the tile?</p>

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

43 <p>The perimeter of the tile is 92 units.</p>

44 <h3>Explanation</h3>

45 <p>The side length of the tile is √529 = 23.</p>

46 <p>The perimeter of a square is 4 times the side length, so the perimeter is 4 × 23 = 92 units.</p>

47 <p>Well explained 👍</p>

48 <h3>Problem 3</h3>

49 <p>Calculate 2 × √529.</p>

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

51 <p>46</p>

52 <h3>Explanation</h3>

53 <p>The square root of 529 is 23.</p>

54 <p>Therefore, 2 × √529 = 2 × 23 = 46.</p>

55 <p>Well explained 👍</p>

56 <h3>Problem 4</h3>

57 <p>What is the square root of (529 - 4)?</p>

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

59 <p>The square root is 22.</p>

60 <h3>Explanation</h3>

61 <p>First, find the difference: 529 - 4 = 525.</p>

62 <p>The square root of 525 is approximately 22.91, but this question seems to have an error as 525 is not a perfect square.</p>

63 <p>The correct context would be using perfect squares.</p>

64 <p>Well explained 👍</p>

65 <h3>Problem 5</h3>

66 <p>What is the perimeter of a rectangle if its length ‘l’ is √529 units and the width ‘w’ is 10 units?</p>

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

68 <p>The perimeter of the rectangle is 66 units.</p>

69 <h3>Explanation</h3>

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

71 <p>Perimeter = 2 × (√529 + 10) = 2 × (23 + 10) = 2 × 33 = 66 units.</p>

72 <p>Well explained 👍</p>

73 <h2>FAQ on Square Root of 529</h2>

74 <h3>1.What is √529 in its simplest form?</h3>

75 <p>The prime factorization of 529 is 23 × 23, so the simplest form of √529 is 23.</p>

76 <h3>2.Is 529 a perfect square?</h3>

77 <p>Yes, 529 is a perfect square because it can be expressed as 23 × 23.</p>

78 <h3>3.What are the factors of 529?</h3>

79 <p>The factors of 529 are 1, 23, and 529.</p>

80 <h3>4.Calculate the square of 23.</h3>

81 <p>The square of 23 is 529, since 23 × 23 = 529.</p>

82 <h3>5.Is 529 a prime number?</h3>

83 <p>No, 529 is not a<a>prime number</a>because it has more than two factors.</p>

84 <h2>Important Glossaries for the Square Root of 529</h2>

85 <ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: 232 = 529 and the inverse of the square is the square root, which is √529 = 23.</li>

86 </ul><ul><li><strong>Perfect square:</strong>A number that can be expressed as the product of an integer with itself.</li>

87 </ul><ul><li><strong>Rational number:</strong>A number that can be expressed in the form p/q, where p and q are integers and q ≠ 0.</li>

88 </ul><ul><li><strong>Prime factorization:</strong>The process of expressing a number as the product of its prime factors.</li>

89 </ul><ul><li><strong>Perimeter:</strong>The total distance around a two-dimensional shape, such as a square or rectangle.</li>

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

91 <p>▶</p>

92 <h2>Jaskaran Singh Saluja</h2>

93 <h3>About the Author</h3>

94 <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>

95 <h3>Fun Fact</h3>

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