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

3 <p>If a number is multiplied by itself, the result is a square. The inverse of squaring a number is finding its square root. The square root has applications in fields like vehicle design, finance, and more. Here, we will discuss the square root of 984.</p>

4 <h2>What is the Square Root of 984?</h2>

5 <p>The<a>square</a>root is the inverse operation of squaring a<a>number</a>. Since 984 is not a<a>perfect square</a>, its square root is expressed in both radical and exponential forms. In radical form, it is √984, while in<a>exponential form</a>, it is expressed as (984)(1/2). The approximate value of √984 is 31.368, which is an<a>irrational number</a>because it cannot be expressed as a<a>fraction</a>p/q, where p and q are<a>integers</a>and q ≠ 0.</p>

6 <h2>Finding the Square Root of 984</h2>

7 <p>The<a>prime factorization</a>method works well for perfect squares. For non-perfect squares like 984, other methods such as the<a>long division</a>method and approximation method are used. Let's explore these methods: -</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 984 by Prime Factorization Method</h2>

12 <p>Prime factorization breaks a number down into its prime<a>factors</a>. Let's examine how 984 is broken down:</p>

13 <p><strong>Step 1:</strong>Finding the prime factors of 984 Breaking it down, we get 2 x 2 x 2 x 3 x 41: 23 x 3 x 41</p>

14 <p><strong>Step 2:</strong>After identifying the prime factors of 984, we attempt to pair them. Since 984 is not a perfect square, the digits cannot be completely paired, making it impossible to calculate using prime factorization alone.</p>

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17 <h2>Square Root of 984 by Long Division Method</h2>

16 <h2>Square Root of 984 by Long Division Method</h2>

18 <p>The long<a>division</a>method is particularly useful for non-perfect square numbers. Here’s how to use it for finding the<a>square root</a>of 984:</p>

17 <p>The long<a>division</a>method is particularly useful for non-perfect square numbers. Here’s how to use it for finding the<a>square root</a>of 984:</p>

19 <p><strong>Step 1:</strong>Group the number from right to left. For 984, we group it as 98 and 4.</p>

18 <p><strong>Step 1:</strong>Group the number from right to left. For 984, we group it as 98 and 4.</p>

20 <p><strong>Step 2:</strong>Find n whose square is<a>less than</a>or equal to 98. n=9 because 9^2=81, which is less than 98. The<a>quotient</a>is 9, and the<a>remainder</a>is 17 after subtracting 81 from 98.</p>

19 <p><strong>Step 2:</strong>Find n whose square is<a>less than</a>or equal to 98. n=9 because 9^2=81, which is less than 98. The<a>quotient</a>is 9, and the<a>remainder</a>is 17 after subtracting 81 from 98.</p>

21 <p><strong>Step 3:</strong>Bring down the next pair, 4, making the new<a>dividend</a>174. Add the last<a>divisor</a>(9) to itself, making it 18.</p>

20 <p><strong>Step 3:</strong>Bring down the next pair, 4, making the new<a>dividend</a>174. Add the last<a>divisor</a>(9) to itself, making it 18.</p>

22 <p><strong>Step 4:</strong>Find a digit which when added to 180 and multiplied by the same digit gives a product less than or equal to 1744. That digit is 9, because 189 x 9 = 1701.</p>

21 <p><strong>Step 4:</strong>Find a digit which when added to 180 and multiplied by the same digit gives a product less than or equal to 1744. That digit is 9, because 189 x 9 = 1701.</p>

23 <p><strong>Step 5:</strong>Subtract 1701 from 1744, resulting in 43.</p>

22 <p><strong>Step 5:</strong>Subtract 1701 from 1744, resulting in 43.</p>

24 <p><strong>Step 6:</strong>Since the remainder is less than the divisor, add a decimal point and continue the process.</p>

23 <p><strong>Step 6:</strong>Since the remainder is less than the divisor, add a decimal point and continue the process.</p>

25 <p><strong>Step 7:</strong>Continue these steps until the desired decimal accuracy is reached. The square root of 984 is approximately 31.368.</p>

24 <p><strong>Step 7:</strong>Continue these steps until the desired decimal accuracy is reached. The square root of 984 is approximately 31.368.</p>

26 <h2>Square Root of 984 by Approximation Method</h2>

25 <h2>Square Root of 984 by Approximation Method</h2>

27 <p>The approximation method is a straightforward way to find square roots. Here's how to approximate the square root of 984:</p>

26 <p>The approximation method is a straightforward way to find square roots. Here's how to approximate the square root of 984:</p>

28 <p><strong>Step 1:</strong>Identify the closest perfect squares. 961 (312) and 1024 (322) are the nearest perfect squares to 984. Thus, √984 is between 31 and 32.</p>

27 <p><strong>Step 1:</strong>Identify the closest perfect squares. 961 (312) and 1024 (322) are the nearest perfect squares to 984. Thus, √984 is between 31 and 32.</p>

29 <p><strong>Step 2:</strong>Use interpolation to find a more precise value: (984 - 961) / (1024 - 961) = 23 / 63 ≈ 0.365 Add the result to 31, giving 31 + 0.365 = 31.365</p>

28 <p><strong>Step 2:</strong>Use interpolation to find a more precise value: (984 - 961) / (1024 - 961) = 23 / 63 ≈ 0.365 Add the result to 31, giving 31 + 0.365 = 31.365</p>

30 <p>Thus, √984 is approximately 31.365.</p>

29 <p>Thus, √984 is approximately 31.365.</p>

31 <h2>Common Mistakes and How to Avoid Them in the Square Root of 984</h2>

30 <h2>Common Mistakes and How to Avoid Them in the Square Root of 984</h2>

32 <p>Students often make errors while finding square roots, such as overlooking negative roots or skipping steps in long division. Here are some common mistakes and solutions:</p>

31 <p>Students often make errors while finding square roots, such as overlooking negative roots or skipping steps in long division. Here are some common mistakes and solutions:</p>

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33 <h3>Problem 1</h3>

34 <p>If a square has a side length of √984, what is its area?</p>

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

36 <p>The area of the square is approximately 984 square units.</p>

37 <h3>Explanation</h3>

38 <p>The area of a square is calculated as side².</p>

39 <p>If the side length is √984, then the area is (√984)² = 984 square units.</p>

40 <p>Well explained 👍</p>

41 <h3>Problem 2</h3>

42 <p>A garden has an area of 984 square feet. What is the length of one side of the garden?</p>

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

44 <p>The side length of the garden is approximately 31.368 feet.</p>

45 <h3>Explanation</h3>

46 <p>The side length of the garden is the square root of the area.</p>

47 <p>Thus, the side length is √984 ≈ 31.368 feet.</p>

48 <p>Well explained 👍</p>

49 <h3>Problem 3</h3>

50 <p>Calculate 5 times the square root of 984.</p>

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

52 <p>The result is approximately 156.84.</p>

53 <h3>Explanation</h3>

54 <p>First, find the square root of 984, which is approximately 31.368, then multiply it by 5: 31.368 x 5 ≈ 156.84.</p>

55 <p>Well explained 👍</p>

56 <h3>Problem 4</h3>

57 <p>What is the square root of (984 + 16)?</p>

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

59 <p>The square root is approximately 32.</p>

60 <h3>Explanation</h3>

61 <p>Calculate the sum: 984 + 16 = 1000.</p>

62 <p>Then find the square root: √1000 ≈ 31.622.</p>

63 <p>However, considering approximation, it is often rounded to 32 for practical purposes.</p>

64 <p>Well explained 👍</p>

65 <h3>Problem 5</h3>

66 <p>Find the perimeter of a rectangle with length √984 units and width 40 units.</p>

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

68 <p>The perimeter is approximately 142.736 units.</p>

69 <h3>Explanation</h3>

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

71 <p>Length = √984 ≈ 31.368.</p>

72 <p>Therefore, the perimeter = 2 × (31.368 + 40) = 2 × 71.368 = 142.736 units.</p>

73 <p>Well explained 👍</p>

74 <h2>FAQ on Square Root of 984</h2>

75 <h3>1.What is √984 in its simplest form?</h3>

76 <p>The prime factorization of 984 is 23 x 3 x 41, so the simplest form of √984 remains in its<a>decimal</a>approximation: approximately 31.368.</p>

77 <h3>2.What are the factors of 984?</h3>

78 <p>The factors of 984 are 1, 2, 3, 4, 6, 8, 12, 24, 41, 82, 123, 164, 246, 328, 492, and 984.</p>

79 <h3>3.Calculate the square of 984.</h3>

80 <p>The square of 984 is 984 × 984 = 968,256.</p>

81 <h3>4.Is 984 a prime number?</h3>

82 <h3>5.Which numbers is 984 divisible by?</h3>

83 <p>984 is divisible by several numbers, including 1, 2, 3, 4, 6, 8, 12, 24, 41, 82, 123, 164, 246, 328, 492, and 984.</p>

84 <h2>Important Glossaries for the Square Root of 984</h2>

85 <ul><li>-<strong>Square root:</strong>The square root of a number is a value that, when multiplied by itself, gives the original number. For instance, the square root of 16 is 4, because 4 × 4 = 16. -</li>

86 </ul><ul><li><strong>Irrational number:</strong>A number that cannot be written as a simple fraction; its decimal form is non-terminating and non-repeating. Example: √2. -</li>

87 </ul><ul><li><strong>Prime factorization:</strong>The expression of a number as a product of its prime numbers. -</li>

88 </ul><ul><li><strong>Perfect square:</strong>A number that is the square of an integer. Example: 49, because 7 × 7 = 49. -</li>

89 </ul><ul><li><strong>Long division method:</strong>A step-by-step process of dividing numbers to find the square root of non-perfect squares.</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>