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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 996.</p>

4 <h2>What is the Square Root of 996?</h2>

5 <p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 996 is not a<a>perfect square</a>. The square root of 996 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √996, whereas (996)^(1/2) in the exponential form. √996 ≈ 31.542, 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 996</h2>

7 <p>The<a>prime factorization</a>method is used for perfect square numbers. However, for non-perfect square numbers, methods like the<a>long division</a>method and approximation method are used. Let us now learn the following methods: - Prime factorization method - Long division method - Approximation method</p>

8 <h2>Square Root of 996 by Prime Factorization Method</h2>

9 <p>The<a>product</a>of prime<a>factors</a>is the prime factorization of a number. Now let us look at how 996 is broken down into its prime factors: Step 1: Finding the prime factors of 996 Breaking it down, we get 2 × 2 × 3 × 83: 2^2 × 3^1 × 83^1 Step 2: Now we have found out the prime factors of 996. The second step is to make pairs of those prime factors. Since 996 is not a perfect square, the digits of the number can’t be grouped into pairs for all factors. Therefore, calculating 996 using prime factorization involves approximating or using other methods.</p>

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12 <h2>Square Root of 996 by Long Division Method</h2>

11 <h2>Square Root of 996 by Long Division Method</h2>

13 <p>The long<a>division</a>method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the<a>square root</a>using the long division method, step by step: Step 1: To begin with, group the numbers from right to left. In the case of 996, we group it as 96 and 9. Step 2: Now we need to find n whose square is<a>less than</a>or equal to 9. We choose n as ‘3’ because 3^2 = 9. The<a>quotient</a>is 3, and the<a>remainder</a>is 0. Step 3: Bring down 96, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number: 3 + 3 = 6, which will be our new divisor. Step 4: Find 6n such that 6n × n is less than or equal to 96. We try n = 1, so 61 × 1 = 61. Step 5: Subtract 61 from 96; the difference is 35, and the quotient is 31. Step 6: Since the dividend is less than the divisor, add a decimal point, allowing us to add two zeroes to the dividend. The new dividend is 3500. Step 7: Find the new divisor, which is 629, because 629 × 5 = 3145. Step 8: Subtracting 3145 from 3500, we get the result 355. Step 9: The quotient is now 31.5. Step 10: Continue these steps until we achieve the desired precision. The square root of √996 is approximately 31.542.</p>

12 <p>The long<a>division</a>method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the<a>square root</a>using the long division method, step by step: Step 1: To begin with, group the numbers from right to left. In the case of 996, we group it as 96 and 9. Step 2: Now we need to find n whose square is<a>less than</a>or equal to 9. We choose n as ‘3’ because 3^2 = 9. The<a>quotient</a>is 3, and the<a>remainder</a>is 0. Step 3: Bring down 96, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number: 3 + 3 = 6, which will be our new divisor. Step 4: Find 6n such that 6n × n is less than or equal to 96. We try n = 1, so 61 × 1 = 61. Step 5: Subtract 61 from 96; the difference is 35, and the quotient is 31. Step 6: Since the dividend is less than the divisor, add a decimal point, allowing us to add two zeroes to the dividend. The new dividend is 3500. Step 7: Find the new divisor, which is 629, because 629 × 5 = 3145. Step 8: Subtracting 3145 from 3500, we get the result 355. Step 9: The quotient is now 31.5. Step 10: Continue these steps until we achieve the desired precision. The square root of √996 is approximately 31.542.</p>

14 <h2>Square Root of 996 by Approximation Method</h2>

13 <h2>Square Root of 996 by Approximation Method</h2>

15 <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 996 using the approximation method. Step 1: Find the closest perfect square of √996. The smallest perfect square less than 996 is 961, and the largest perfect square more than 996 is 1024. √996 falls somewhere between 31 and 32. Step 2: Apply the<a>formula</a>: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (996 - 961) / (1024 - 961) = 35 / 63 ≈ 0.556. Adding the value to the lower integer, 31 + 0.556 ≈ 31.556, so the square root of 996 is approximately 31.556.</p>

14 <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 996 using the approximation method. Step 1: Find the closest perfect square of √996. The smallest perfect square less than 996 is 961, and the largest perfect square more than 996 is 1024. √996 falls somewhere between 31 and 32. Step 2: Apply the<a>formula</a>: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (996 - 961) / (1024 - 961) = 35 / 63 ≈ 0.556. Adding the value to the lower integer, 31 + 0.556 ≈ 31.556, so the square root of 996 is approximately 31.556.</p>

16 <h2>Common Mistakes and How to Avoid Them in the Square Root of 996</h2>

15 <h2>Common Mistakes and How to Avoid Them in the Square Root of 996</h2>

17 <p>Students often make mistakes while finding the square root, like forgetting about the negative square root or skipping long division steps. Let us look at a few common mistakes and how to avoid them.</p>

16 <p>Students often make mistakes while finding the square root, like forgetting about the negative square root or skipping long division steps. Let us look at a few common mistakes and how to avoid them.</p>

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18 <h3>Problem 1</h3>

19 <p>Can you help Max find the area of a square box if its side length is given as √996?</p>

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

21 <p>The area of the square is approximately 992.016 square units.</p>

22 <h3>Explanation</h3>

23 <p>The area of the square = side^2. The side length is given as √996. Area of the square = side^2 = √996 × √996 ≈ 31.542 × 31.542 ≈ 992.016. Therefore, the area of the square box is approximately 992.016 square units.</p>

24 <p>Well explained 👍</p>

25 <h3>Problem 2</h3>

26 <p>A square-shaped garden measuring 996 square feet is built; if each of the sides is √996, what will be the square feet of half of the garden?</p>

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

28 <p>498 square feet</p>

29 <h3>Explanation</h3>

30 <p>We divide the given area by 2 since the garden is square-shaped. Dividing 996 by 2, we get 498. So, half of the garden measures 498 square feet.</p>

31 <p>Well explained 👍</p>

32 <h3>Problem 3</h3>

33 <p>Calculate √996 × 5.</p>

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

35 <p>Approximately 157.71</p>

36 <h3>Explanation</h3>

37 <p>First, find the square root of 996, which is approximately 31.542. Multiply 31.542 by 5: 31.542 × 5 ≈ 157.71.</p>

38 <p>Well explained 👍</p>

39 <h3>Problem 4</h3>

40 <p>What will be the square root of (996 + 4)?</p>

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

42 <p>The square root is 32.</p>

43 <h3>Explanation</h3>

44 <p>To find the square root, we need to find the sum of (996 + 4). 996 + 4 = 1000, and then √1000 ≈ 31.62 Therefore, the square root of 1000 is approximately ±31.62.</p>

45 <p>Well explained 👍</p>

46 <h3>Problem 5</h3>

47 <p>Find the perimeter of the rectangle if its length ‘l’ is √996 units and the width ‘w’ is 40 units.</p>

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

49 <p>We find the perimeter of the rectangle as approximately 143.084 units.</p>

50 <h3>Explanation</h3>

51 <p>Perimeter of the rectangle = 2 × (length + width) Perimeter = 2 × (√996 + 40) ≈ 2 × (31.542 + 40) ≈ 2 × 71.542 ≈ 143.084 units.</p>

52 <p>Well explained 👍</p>

53 <h2>FAQ on Square Root of 996</h2>

54 <h3>1.What is √996 in its simplest form?</h3>

55 <p>The prime factorization of 996 is 2 × 2 × 3 × 83, so the simplest form of √996 = √(2^2 × 3 × 83).</p>

56 <h3>2.Mention the factors of 996.</h3>

57 <p>Factors of 996 are 1, 2, 3, 4, 6, 12, 83, 166, 249, 332, 498, and 996.</p>

58 <h3>3.Calculate the square of 996.</h3>

59 <p>We get the square of 996 by multiplying the number by itself, that is 996 × 996 = 992016.</p>

60 <h3>4.Is 996 a prime number?</h3>

61 <h3>5.996 is divisible by?</h3>

62 <p>996 has several factors; it is divisible by 1, 2, 3, 4, 6, 12, 83, 166, 249, 332, 498, and 996.</p>

63 <h2>Important Glossaries for the Square Root of 996</h2>

64 <p>Square root: A square root is the inverse operation of squaring a number. Example: 4^2 = 16, so the square root is √16 = 4. Irrational number: An irrational number is a number that cannot be written as a simple fraction, like √996, which cannot be expressed as p/q where p and q are integers and q ≠ 0. Principal square root: Although a number has both positive and negative square roots, the principal square root refers to the non-negative one, which is commonly used in real-world applications. Approximation: This refers to finding a value that is close enough to the right answer, usually with a specified degree of accuracy. For example, √996 ≈ 31.542. Long division method: A step-by-step division process used to find square roots of non-perfect squares by approximating to the desired decimal places.</p>

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

66 <p>▶</p>

67 <h2>Jaskaran Singh Saluja</h2>

68 <h3>About the Author</h3>

69 <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>

70 <h3>Fun Fact</h3>

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