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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 engineering, architecture, and finance. Here, we will discuss the square root of 487.</p>

4 <h2>What is the Square Root of 487?</h2>

5 <p>The<a>square</a>root is the inverse of squaring a<a>number</a>. 487 is not a<a>perfect square</a>. The square root of 487 is expressed in both radical and<a>exponential form</a>. In radical form, it is expressed as √487, whereas in exponential form, it is expressed as (487)^(1/2). √487 ≈ 22.068, 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>

6 <h2>Finding the Square Root of 487</h2>

7 <p>The<a>prime factorization</a>method is used for perfect square numbers. However, for non-perfect square numbers, the<a>long division</a>method and approximation method are used. Let us now learn the following methods:</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 487 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 487 is broken down into its prime factors:</p>

13 <p><strong>Step 1:</strong>Finding the prime factors of 487. 487 is a<a>prime number</a>, so it cannot be broken down further into other prime factors. Thus, it cannot be simplified using the prime factorization method. Calculating the<a>square root</a>of 487 using prime factorization is not feasible.</p>

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16 <h2>Square Root of 487 by Long Division Method</h2>

15 <h2>Square Root of 487 by Long Division Method</h2>

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

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

18 <p><strong>Step 1:</strong>Start by grouping the digits from right to left in pairs. In the case of 487, we have 4 and 87.</p>

17 <p><strong>Step 1:</strong>Start by grouping the digits from right to left in pairs. In the case of 487, we have 4 and 87.</p>

19 <p><strong>Step 2:</strong>Find a number n whose square is<a>less than</a>or equal to 4. This number is 2, because 2 × 2 = 4.</p>

18 <p><strong>Step 2:</strong>Find a number n whose square is<a>less than</a>or equal to 4. This number is 2, because 2 × 2 = 4.</p>

20 <p><strong>Step 3:</strong>Subtract 4 from 4, which leaves a<a>remainder</a>of 0, and bring down the next pair, 87.</p>

19 <p><strong>Step 3:</strong>Subtract 4 from 4, which leaves a<a>remainder</a>of 0, and bring down the next pair, 87.</p>

21 <p><strong>Step 4:</strong>Double the<a>divisor</a>(2) to get 4, and find a new digit (n) such that 4n × n ≤ 87. This digit is 2, because 42 × 2 = 84.</p>

20 <p><strong>Step 4:</strong>Double the<a>divisor</a>(2) to get 4, and find a new digit (n) such that 4n × n ≤ 87. This digit is 2, because 42 × 2 = 84.</p>

22 <p><strong>Step 5:</strong>Subtract 84 from 87, resulting in a remainder of 3.</p>

21 <p><strong>Step 5:</strong>Subtract 84 from 87, resulting in a remainder of 3.</p>

23 <p><strong>Step 6:</strong>Since the<a>dividend</a>is less than the divisor, add a<a>decimal</a>point and bring down a pair of zeros to the remainder to make it 300.</p>

22 <p><strong>Step 6:</strong>Since the<a>dividend</a>is less than the divisor, add a<a>decimal</a>point and bring down a pair of zeros to the remainder to make it 300.</p>

24 <p><strong>Step 7:</strong>The new divisor is 44, and find n such that 44n × n ≤ 300. The number is 6, because 446 × 6 = 2676.</p>

23 <p><strong>Step 7:</strong>The new divisor is 44, and find n such that 44n × n ≤ 300. The number is 6, because 446 × 6 = 2676.</p>

25 <p><strong>Step 8:</strong>Subtract 2676 from 3000 to get a remainder of 324.</p>

24 <p><strong>Step 8:</strong>Subtract 2676 from 3000 to get a remainder of 324.</p>

26 <p><strong>Step 9:</strong>Continue the process to get the desired precision.</p>

25 <p><strong>Step 9:</strong>Continue the process to get the desired precision.</p>

27 <p>So the square root of √487 ≈ 22.068.</p>

26 <p>So the square root of √487 ≈ 22.068.</p>

28 <h2>Square Root of 487 by Approximation Method</h2>

27 <h2>Square Root of 487 by Approximation Method</h2>

29 <p>The approximation method is another method for finding square roots. Now let us learn how to find the square root of 487 using the approximation method.</p>

28 <p>The approximation method is another method for finding square roots. Now let us learn how to find the square root of 487 using the approximation method.</p>

30 <p><strong>Step 1:</strong>Determine the closest perfect squares surrounding √487. The closest perfect squares are 484 (22^2) and 529 (23^2). Thus, √487 lies between 22 and 23.</p>

29 <p><strong>Step 1:</strong>Determine the closest perfect squares surrounding √487. The closest perfect squares are 484 (22^2) and 529 (23^2). Thus, √487 lies between 22 and 23.</p>

31 <p><strong>Step 2:</strong>Apply the<a>formula</a>: (Given number - smallest perfect square) ÷ (Greater perfect square - smallest perfect square). Applying the formula: (487 - 484) ÷ (529 - 484) = 3 ÷ 45 ≈ 0.067. Adding this to 22 gives us 22 + 0.067 ≈ 22.067.</p>

30 <p><strong>Step 2:</strong>Apply the<a>formula</a>: (Given number - smallest perfect square) ÷ (Greater perfect square - smallest perfect square). Applying the formula: (487 - 484) ÷ (529 - 484) = 3 ÷ 45 ≈ 0.067. Adding this to 22 gives us 22 + 0.067 ≈ 22.067.</p>

32 <p>Hence, the square root of 487 is approximately 22.067.</p>

31 <p>Hence, the square root of 487 is approximately 22.067.</p>

33 <h2>Common Mistakes and How to Avoid Them in the Square Root of 487</h2>

32 <h2>Common Mistakes and How to Avoid Them in the Square Root of 487</h2>

34 <p>Students often make mistakes while finding square roots, such as forgetting about the negative square root or skipping important steps in the long division method. Here are a few common mistakes to avoid:</p>

33 <p>Students often make mistakes while finding square roots, such as forgetting about the negative square root or skipping important steps in the long division method. Here are a few common mistakes to avoid:</p>

34 + <h2>Download Worksheets</h2>

35 <h3>Problem 1</h3>

36 <p>Can you help Sarah find the area of a square box if its side length is given as √487?</p>

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

38 <p>The area of the square is approximately 487 square units.</p>

39 <h3>Explanation</h3>

40 <p>The area of a square is calculated as side^2.</p>

41 <p>Given the side length is √487, the area is √487 × √487 = 487 square units.</p>

42 <p>Well explained 👍</p>

43 <h3>Problem 2</h3>

44 <p>A square-shaped garden measures 487 square feet. If each side is √487, what will be the square feet of half of the garden?</p>

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

46 <p>243.5 square feet.</p>

47 <h3>Explanation</h3>

48 <p>To find half the area of the garden, divide the total area by 2: 487 ÷ 2 = 243.5 square feet.</p>

49 <p>Well explained 👍</p>

50 <h3>Problem 3</h3>

51 <p>Calculate √487 × 5.</p>

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

53 <p>Approximately 110.34.</p>

54 <h3>Explanation</h3>

55 <p>First, find the square root of 487, which is approximately 22.068.</p>

56 <p>Then, multiply this by 5: 22.068 × 5 ≈ 110.34.</p>

57 <p>Well explained 👍</p>

58 <h3>Problem 4</h3>

59 <p>What will be the square root of (484 + 3)?</p>

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

61 <p>The square root is approximately 22.07.</p>

62 <h3>Explanation</h3>

63 <p>To find the square root, first calculate the sum: 484 + 3 = 487.</p>

64 <p>The square root of 487 is approximately 22.07.</p>

65 <p>Well explained 👍</p>

66 <h3>Problem 5</h3>

67 <p>Find the perimeter of a rectangle if its length ‘l’ is √487 units and the width ‘w’ is 10 units.</p>

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

69 <p>The perimeter of the rectangle is approximately 64.136 units.</p>

70 <h3>Explanation</h3>

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

72 <p>Perimeter = 2 × (√487 + 10) ≈ 2 × (22.068 + 10) = 2 × 32.068 ≈ 64.136 units.</p>

73 <p>Well explained 👍</p>

74 <h2>FAQ on Square Root of 487</h2>

75 <h3>1.What is √487 in its simplest form?</h3>

76 <p>Since 487 is a prime number, √487 cannot be simplified and remains as √487.</p>

77 <h3>2.Calculate the square of 487.</h3>

78 <p>The square of 487 is 487 × 487 = 237,169.</p>

79 <h3>3.Is 487 a prime number?</h3>

80 <p>Yes, 487 is a prime number because it has no factors other than 1 and itself.</p>

81 <h3>4.What are the factors of 487?</h3>

82 <p>The factors of 487 are 1 and 487, as it is a prime number.</p>

83 <h3>5.487 is divisible by?</h3>

84 <p>487 is only divisible by 1 and 487.</p>

85 <h2>Important Glossaries for the Square Root of 487</h2>

86 <ul><li><strong>Square root:</strong>A square root is the inverse of squaring a number. Example: 4^2 = 16, and the inverse is the square root, √16 = 4. </li>

87 <li><strong>Irrational number:</strong>A number that cannot be expressed as a simple fraction (p/q, where p and q are integers and q ≠ 0), such as √487. </li>

88 <li><strong>Prime number:</strong>A number greater than 1 with no divisors other than 1 and itself, such as 487. </li>

89 <li><strong>Decimal:</strong>A number that includes a fractional part, such as 22.068. </li>

90 <li><strong>Long division method:</strong>A technique for finding the square root of non-perfect squares by dividing the number into smaller, more manageable parts.</li>

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

92 <p>▶</p>

93 <h2>Jaskaran Singh Saluja</h2>

94 <h3>About the Author</h3>

95 <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>

96 <h3>Fun Fact</h3>

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