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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 various fields such as vehicle design, finance, etc. Here, we will discuss the square root of 997.</p>

4 <h2>What is the Square Root of 997?</h2>

5 <p>The<a>square</a>root is the inverse of squaring a<a>number</a>. 997 is not a<a>perfect square</a>. The square root of 997 is expressed in both radical and exponential forms. In radical form, it is expressed as √997, whereas (997)(1/2) in<a>exponential form</a>. √997 ≈ 31.575, 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 997</h2>

7 <p>The<a>prime factorization</a>method is used for perfect square numbers. However, for non-perfect square numbers, the long-<a>division</a>method and approximation method are used. Let us now learn the following 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 997 by Prime Factorization Method</h2>

12 <p>The prime factorization of a number is the<a>product</a>of its prime<a>factors</a>. Now, let us look at how 997 is broken down into its prime factors.</p>

13 <p><strong>Step 1:</strong>Finding the prime factors of 997</p>

14 <p>997 is a<a>prime number</a>itself, and thus cannot be broken down further. As it is not a perfect square, calculating the<a>square root</a>using prime factorization is not feasible.</p>

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17 <h2>Square Root of 997 by Long Division Method</h2>

16 <h2>Square Root of 997 by Long Division Method</h2>

18 <p>The<a>long 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>

17 <p>The<a>long 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>

19 <p><strong>Step 1:</strong>To begin with, group the numbers from right to left. For 997, it can be grouped as 9 and 97.</p>

18 <p><strong>Step 1:</strong>To begin with, group the numbers from right to left. For 997, it can be grouped as 9 and 97.</p>

20 <p><strong>Step 2:</strong>Find n whose square is ≤ 9. We can take n as 3 because 3 × 3 = 9. Subtracting gives a<a>remainder</a>of 0, and the<a>quotient</a>is 3.</p>

19 <p><strong>Step 2:</strong>Find n whose square is ≤ 9. We can take n as 3 because 3 × 3 = 9. Subtracting gives a<a>remainder</a>of 0, and the<a>quotient</a>is 3.</p>

21 <p><strong>Step 3:</strong>Bring down 97, making the new<a>dividend</a>97.</p>

20 <p><strong>Step 3:</strong>Bring down 97, making the new<a>dividend</a>97.</p>

22 <p><strong>Step 4:</strong>Add the old<a>divisor</a>with the same number: 3 + 3 = 6, which will be our new divisor.</p>

21 <p><strong>Step 4:</strong>Add the old<a>divisor</a>with the same number: 3 + 3 = 6, which will be our new divisor.</p>

23 <p><strong>Step 5:</strong>The new divisor will be 6n. Find n such that 6n × n ≤ 97. Choose n as 1, since 61 × 1 = 61.</p>

22 <p><strong>Step 5:</strong>The new divisor will be 6n. Find n such that 6n × n ≤ 97. Choose n as 1, since 61 × 1 = 61.</p>

24 <p><strong>Step 6:</strong>Subtract 61 from 97 to get 36, and the quotient is 31.</p>

23 <p><strong>Step 6:</strong>Subtract 61 from 97 to get 36, and the quotient is 31.</p>

25 <p><strong>Step 7:</strong>Since the dividend is<a>less than</a>the divisor, add a<a>decimal</a>point and bring down two zeros to make the new dividend 3600.</p>

24 <p><strong>Step 7:</strong>Since the dividend is<a>less than</a>the divisor, add a<a>decimal</a>point and bring down two zeros to make the new dividend 3600.</p>

26 <p><strong>Step 8:</strong>The new divisor is 631, as 631 × 5 = 3155.</p>

25 <p><strong>Step 8:</strong>The new divisor is 631, as 631 × 5 = 3155.</p>

27 <p><strong>Step 9:</strong>Subtracting 3155 from 3600 gives the result 445.</p>

26 <p><strong>Step 9:</strong>Subtracting 3155 from 3600 gives the result 445.</p>

28 <p><strong>Step 10:</strong>The quotient is 31.5.</p>

27 <p><strong>Step 10:</strong>The quotient is 31.5.</p>

29 <p><strong>Step 11:</strong>Continue these steps until reaching the desired decimal places. So, the square root of √997 is approximately 31.575.</p>

28 <p><strong>Step 11:</strong>Continue these steps until reaching the desired decimal places. So, the square root of √997 is approximately 31.575.</p>

30 <h2>Square Root of 997 by Approximation Method</h2>

29 <h2>Square Root of 997 by Approximation Method</h2>

31 <p>The approximation method is another way to find square roots. It is an easy method to find the square root of a given number. Let us learn how to find the square root of 997 using the approximation method.</p>

30 <p>The approximation method is another way to find square roots. It is an easy method to find the square root of a given number. Let us learn how to find the square root of 997 using the approximation method.</p>

32 <p><strong>Step 1:</strong>Identify the perfect squares closest to √997. The perfect square smaller than 997 is 961, and the perfect square larger than 997 is 1024. √997 falls between 31 and 32.</p>

31 <p><strong>Step 1:</strong>Identify the perfect squares closest to √997. The perfect square smaller than 997 is 961, and the perfect square larger than 997 is 1024. √997 falls between 31 and 32.</p>

33 <p><strong>Step 2:</strong>Use the<a>formula</a>(Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (997 - 961) / (1024 - 961) = 36 / 63 ≈ 0.57.</p>

32 <p><strong>Step 2:</strong>Use the<a>formula</a>(Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (997 - 961) / (1024 - 961) = 36 / 63 ≈ 0.57.</p>

34 <p>Adding this to the lower bound of the square root: 31 + 0.57 = 31.57. Therefore, the square root of 997 is approximately 31.57.</p>

33 <p>Adding this to the lower bound of the square root: 31 + 0.57 = 31.57. Therefore, the square root of 997 is approximately 31.57.</p>

35 <h2>Common Mistakes and How to Avoid Them in the Square Root of 997</h2>

34 <h2>Common Mistakes and How to Avoid Them in the Square Root of 997</h2>

36 <p>Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division methods. Let us look at a few common mistakes in detail.</p>

35 <p>Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division methods. Let us look at a few common mistakes in detail.</p>

36 + <h2>Download Worksheets</h2>

37 <h3>Problem 1</h3>

38 <p>Can you help Max find the area of a square box if its side length is given as √997?</p>

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

40 <p>The area of the square is 994.29 square units.</p>

41 <h3>Explanation</h3>

42 <p>The area of a square = side².</p>

43 <p>The side length is given as √997.</p>

44 <p>Area = side² = √997 × √997 = 31.575 × 31.575 ≈ 994.29.</p>

45 <p>Therefore, the area of the square box is approximately 994.29 square units.</p>

46 <p>Well explained 👍</p>

47 <h3>Problem 2</h3>

48 <p>A square-shaped building measuring 997 square feet is built; if each of the sides is √997, what will be the square feet of half of the building?</p>

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

50 <p>Approximately 498.5 square feet</p>

51 <h3>Explanation</h3>

52 <p>Since the building is square-shaped, we can divide the given area by 2.</p>

53 <p>Dividing 997 by 2 gives approximately 498.5.</p>

54 <p>So, half of the building measures approximately 498.5 square feet.</p>

55 <p>Well explained 👍</p>

56 <h3>Problem 3</h3>

57 <p>Calculate √997 × 5.</p>

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

59 <p>Approximately 157.875</p>

60 <h3>Explanation</h3>

61 <p>First, find the square root of 997, which is approximately 31.575.</p>

62 <p>Then multiply 31.575 by 5.</p>

63 <p>So, 31.575 × 5 ≈ 157.875.</p>

64 <p>Well explained 👍</p>

65 <h3>Problem 4</h3>

66 <p>What will be the square root of (986 + 11)?</p>

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

68 <p>The square root is approximately 31.575.</p>

69 <h3>Explanation</h3>

70 <p>To find the square root, sum (986 + 11), which equals 997.</p>

71 <p>√997 is approximately 31.575.</p>

72 <p>Therefore, the square root of (986 + 11) is approximately ±31.575.</p>

73 <p>Well explained 👍</p>

74 <h3>Problem 5</h3>

75 <p>Find the perimeter of the rectangle if its length ‘l’ is √997 units and the width ‘w’ is 38 units.</p>

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

77 <p>The perimeter of the rectangle is approximately 139.15 units.</p>

78 <h3>Explanation</h3>

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

80 <p>Perimeter = 2 × (√997 + 38) ≈ 2 × (31.575 + 38) ≈ 2 × 69.575 ≈ 139.15 units.</p>

81 <p>Well explained 👍</p>

82 <h2>FAQ on Square Root of 997</h2>

83 <h3>1.What is √997 in its simplest form?</h3>

84 <p>Since 997 is a prime number, its simplest form is just √997.</p>

85 <h3>2.Mention the factors of 997.</h3>

86 <p>Since 997 is a prime number, its only factors are 1 and 997.</p>

87 <h3>3.Calculate the square of 997.</h3>

88 <p>We get the square of 997 by multiplying the number by itself, that is 997 × 997 = 994009.</p>

89 <h3>4.Is 997 a prime number?</h3>

90 <p>Yes, 997 is a prime number, as it has only two factors: 1 and 997.</p>

91 <h3>5.Is 997 divisible by any integer other than 1 and itself?</h3>

92 <p>No, 997 is not divisible by any integer other than 1 and 997, confirming it is a prime number.</p>

93 <h2>Important Glossaries for the Square Root of 997</h2>

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

95 </ul><ul><li><strong>Irrational Number:</strong>An irrational number is one that cannot be expressed in the form p/q, where q is not equal to zero and p and q are integers.</li>

96 </ul><ul><li><strong>Prime Number:</strong>A prime number is a number greater than 1 with no divisors other than 1 and itself. For example, 2, 3, 5, 7, 11, etc.</li>

97 </ul><ul><li><strong>Long Division Method:</strong>A procedure used to find the square root of non-perfect squares by dividing the number into pairs and solving iteratively.</li>

98 </ul><ul><li><strong>Decimal:</strong>If a number has both a whole number and a fractional part, it is called a decimal. For example: 7.86, 8.65, and 9.42 are decimals.</li>

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

100 <p>▶</p>

101 <h2>Jaskaran Singh Saluja</h2>

102 <h3>About the Author</h3>

103 <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>

104 <h3>Fun Fact</h3>

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