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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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 87.</p>

4 <h2>What is the Square Root of 87?</h2>

5 <p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 87 is not a<a>perfect square</a>. The square root of 87 is expressed in both radical and<a>exponential form</a>.</p>

6 <p>In the radical form, it is expressed as √87, whereas (87)(1/2) in the exponential form. √87 ≈ 9.327, which is an<a>irrational number</a>because it cannot be expressed in the form of p/q, where p and q are<a>integers</a>and q ≠ 0.</p>

7 <h2>Finding the Square Root of 87</h2>

8 <p>The<a>prime factorization</a>method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where the<a>long division</a>method and approximation method are used. Let us now learn the following methods:</p>

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

10 <li>Long division method</li>

11 <li>Approximation method</li>

12 </ol><h2>Square Root of 87 by Prime Factorization Method</h2>

13 <p>The<a>product</a>of prime<a>factors</a>is the prime factorization of a number. Now let us look at how 87 is broken down into its prime factors.</p>

14 <p><strong>Step 1:</strong>Finding the prime factors of 87 Breaking it down, we get 3 x 29.</p>

15 <p><strong>Step 2:</strong>Now we found out the prime factors of 87. The second step is to make pairs of those prime factors. Since 87 is not a perfect square, the digits of the number can’t be grouped in pairs.</p>

16 <p>Therefore, calculating 87 using prime factorization is not possible for finding an exact integer result.</p>

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19 <h2>Square Root of 87 by Long Division Method</h2>

18 <h2>Square Root of 87 by Long Division Method</h2>

20 <p>The long<a>division</a>method is particularly used for non-perfect square numbers. Let us now learn how to find the<a>square root</a>using the long division method, step by step.</p>

19 <p>The long<a>division</a>method is particularly used for non-perfect square numbers. Let us now learn how to find the<a>square root</a>using the long division method, step by step.</p>

21 <p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 87, we do not need to group since it is a two-digit number.</p>

20 <p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 87, we do not need to group since it is a two-digit number.</p>

22 <p><strong>Step 2:</strong>Now we need to find n whose square is<a>less than</a>or equal to 87. We can say n as ‘9’ because 9 x 9 = 81, which is less than 87. Now the<a>quotient</a>is 9, and the<a>remainder</a>is 87 - 81 = 6.</p>

21 <p><strong>Step 2:</strong>Now we need to find n whose square is<a>less than</a>or equal to 87. We can say n as ‘9’ because 9 x 9 = 81, which is less than 87. Now the<a>quotient</a>is 9, and the<a>remainder</a>is 87 - 81 = 6.</p>

23 <p><strong>Step 3:</strong>Since the<a>dividend</a>is less than the<a>divisor</a>, add a decimal point to the quotient and bring down a pair of zeroes to the remainder. Now the new dividend is 600.</p>

22 <p><strong>Step 3:</strong>Since the<a>dividend</a>is less than the<a>divisor</a>, add a decimal point to the quotient and bring down a pair of zeroes to the remainder. Now the new dividend is 600.</p>

24 <p><strong>Step 4:</strong>Double the quotient (9) and write it as 18. Now find a digit x such that 18x x x is less than or equal to 600. Let's try x = 3, giving us 183 x 3 = 549.</p>

23 <p><strong>Step 4:</strong>Double the quotient (9) and write it as 18. Now find a digit x such that 18x x x is less than or equal to 600. Let's try x = 3, giving us 183 x 3 = 549.</p>

25 <p><strong>Step 5:</strong>Subtract 549 from 600, and the remainder is 51. The quotient is now 9.3.</p>

24 <p><strong>Step 5:</strong>Subtract 549 from 600, and the remainder is 51. The quotient is now 9.3.</p>

26 <p><strong>Step 6:</strong>Continue the process by bringing down more pairs of zeroes until you achieve the desired decimal precision.</p>

25 <p><strong>Step 6:</strong>Continue the process by bringing down more pairs of zeroes until you achieve the desired decimal precision.</p>

27 <p>So the square root of √87 is approximately 9.327.</p>

26 <p>So the square root of √87 is approximately 9.327.</p>

28 <h2>Square Root of 87 by Approximation Method</h2>

27 <h2>Square Root of 87 by Approximation Method</h2>

29 <p>The approximation method is an easy method to find the square root of a given number. Now let us learn how to find the square root of 87 using the approximation method.</p>

28 <p>The approximation method is an easy method to find the square root of a given number. Now let us learn how to find the square root of 87 using the approximation method.</p>

30 <p><strong>Step 1:</strong>Identify the closest perfect squares around 87. The nearest perfect squares are 81 (9^2) and 100 (10^2). √87 falls between 9 and 10.</p>

29 <p><strong>Step 1:</strong>Identify the closest perfect squares around 87. The nearest perfect squares are 81 (9^2) and 100 (10^2). √87 falls between 9 and 10.</p>

31 <p><strong>Step 2:</strong>Apply the<a>formula</a>: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square) (87 - 81) / (100 - 81) = 6 / 19 ≈ 0.316</p>

30 <p><strong>Step 2:</strong>Apply the<a>formula</a>: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square) (87 - 81) / (100 - 81) = 6 / 19 ≈ 0.316</p>

32 <p>Adding this to the smaller perfect square root gives us 9 + 0.316 = 9.316,</p>

31 <p>Adding this to the smaller perfect square root gives us 9 + 0.316 = 9.316,</p>

33 <p>so the square root of 87 is approximately 9.316.</p>

32 <p>so the square root of 87 is approximately 9.316.</p>

34 <h2>Common Mistakes and How to Avoid Them in the Square Root of 87</h2>

33 <h2>Common Mistakes and How to Avoid Them in the Square Root of 87</h2>

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

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

35 + <h2>Download Worksheets</h2>

36 <h3>Problem 1</h3>

37 <p>Can you help Max find the area of a square box if its side length is given as √87?</p>

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

39 <p>The area of the square is approximately 87 square units.</p>

40 <h3>Explanation</h3>

41 <p>The area of the square = side2. The side length is given as √87. Area of the square = side2 = √87 x √87 = 87.</p>

42 <p>Therefore, the area of the square box is approximately 87 square units.</p>

43 <p>Well explained 👍</p>

44 <h3>Problem 2</h3>

45 <p>A square-shaped building measuring 87 square feet is built; if each of the sides is √87, what will be the square feet of half of the building?</p>

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

47 <p>43.5 square feet</p>

48 <h3>Explanation</h3>

49 <p>We can just divide the given area by 2 as the building is square-shaped. Dividing 87 by 2 = 43.5.</p>

50 <p>So half of the building measures 43.5 square feet.</p>

51 <p>Well explained 👍</p>

52 <h3>Problem 3</h3>

53 <p>Calculate √87 x 5.</p>

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

55 <p>46.635</p>

56 <h3>Explanation</h3>

57 <p>The first step is to find the square root of 87, which is approximately 9.327.</p>

58 <p>The second step is to multiply 9.327 by 5. So, 9.327 x 5 ≈ 46.635.</p>

59 <p>Well explained 👍</p>

60 <h3>Problem 4</h3>

61 <p>What will be the square root of (81 + 6)?</p>

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

63 <p>The square root is 9.</p>

64 <h3>Explanation</h3>

65 <p>To find the square root, we need to find the sum of (81 + 6). 81 + 6 = 87, and then √87 ≈ 9.327.</p>

66 <p>However, if considering (81 + 6) = 87, and for simplicity, this is just an example setup; the value of √87 is approximately 9.327.</p>

67 <p>Well explained 👍</p>

68 <h3>Problem 5</h3>

69 <p>Find the perimeter of the rectangle if its length ‘l’ is √87 units and the width ‘w’ is 38 units.</p>

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

71 <p>The perimeter of the rectangle is approximately 94.654 units.</p>

72 <h3>Explanation</h3>

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

74 <p>Perimeter = 2 × (√87 + 38) ≈ 2 × (9.327 + 38) ≈ 2 × 47.327 ≈ 94.654 units.</p>

75 <p>Well explained 👍</p>

76 <h2>FAQ on Square Root of 87</h2>

77 <h3>1.What is √87 in its simplest form?</h3>

78 <p>The prime factorization of 87 is 3 x 29, so the simplest form of √87 remains √87, as it cannot be further simplified to a simpler radical form.</p>

79 <h3>2.Mention the factors of 87.</h3>

80 <p>Factors of 87 are 1, 3, 29, and 87.</p>

81 <h3>3.Calculate the square of 87.</h3>

82 <p>We get the square of 87 by multiplying the number by itself, that is 87 x 87 = 7569.</p>

83 <h3>4.Is 87 a prime number?</h3>

84 <h3>5.87 is divisible by?</h3>

85 <p>87 is divisible by 1, 3, 29, and 87.</p>

86 <h2>Important Glossaries for the Square Root of 87</h2>

87 <ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: 42 = 16, and the inverse of the square is the square root, that is √16 = 4.</li>

88 </ul><ul><li><strong>Irrational number:</strong>An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.</li>

89 </ul><ul><li><strong>Principal square root:</strong>A number has both positive and negative square roots; however, it is always the positive square root that has more prominence due to its uses in the real world. That is the reason it is also known as the principal square root.</li>

90 </ul><ul><li><strong>Long division method:</strong>A method used to find the square root of non-perfect squares by dividing the number into groups of two digits from right to left.</li>

91 </ul><ul><li><strong>Prime factorization:</strong>The process of breaking down a number into its basic prime number factors, which is useful for simplifying radicals.</li>

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

93 <p>▶</p>

94 <h2>Jaskaran Singh Saluja</h2>

95 <h3>About the Author</h3>

96 <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>

97 <h3>Fun Fact</h3>

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