Square Root of 996
2026-02-28 08:27 Diff
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Last updated on August 5, 2025

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.

What is the Square Root of 996?

The square root is the inverse of the square of the number. 996 is not a perfect square. The square root of 996 is expressed in both radical and exponential form. In the radical form, it is expressed as √996, whereas (996)^(1/2) in the exponential form. √996 ≈ 31.542, which is an irrational number because it cannot be expressed in the form of p/q, where p and q are integers and q ≠ 0.

Finding the Square Root of 996

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

Square Root of 996 by Prime Factorization Method

The product of prime factors 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.

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Square Root of 996 by Long Division Method

The long division 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 square root 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 less than or equal to 9. We choose n as ‘3’ because 3^2 = 9. The quotient is 3, and the remainder is 0. Step 3: Bring down 96, which is the new dividend. Add the old divisor 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.

Square Root of 996 by Approximation Method

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 formula: (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.

Common Mistakes and How to Avoid Them in the Square Root of 996

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.

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Problem 1

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

Okay, lets begin

The area of the square is approximately 992.016 square units.

Explanation

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.

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Problem 2

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?

Okay, lets begin

498 square feet

Explanation

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.

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Problem 3

Calculate √996 × 5.

Okay, lets begin

Approximately 157.71

Explanation

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

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Problem 4

What will be the square root of (996 + 4)?

Okay, lets begin

The square root is 32.

Explanation

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.

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Problem 5

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

Okay, lets begin

We find the perimeter of the rectangle as approximately 143.084 units.

Explanation

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

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FAQ on Square Root of 996

1.What is √996 in its simplest form?

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

2.Mention the factors of 996.

Factors of 996 are 1, 2, 3, 4, 6, 12, 83, 166, 249, 332, 498, and 996.

3.Calculate the square of 996.

We get the square of 996 by multiplying the number by itself, that is 996 × 996 = 992016.

4.Is 996 a prime number?

5.996 is divisible by?

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

Important Glossaries for the Square Root of 996

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.

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Jaskaran Singh Saluja

About the Author

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.

Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.