Square Root of 981
2026-02-28 08:52 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-981

338 Learners

Last updated on August 5, 2025

If a number is multiplied by the same number, the result is a square. The inverse of squaring is finding the square root. Square roots are used in fields such as vehicle design, finance, etc. Here, we will discuss the square root of 981.

What is the Square Root of 981?

The square root is the inverse operation of squaring a number. 981 is not a perfect square. The square root of 981 can be expressed in both radical and exponential form. In radical form, it is expressed as √981, whereas in exponential form as (981)(1/2). √981 ≈ 31.32092, which is an irrational number because it cannot be expressed as a fraction of two integers where the denominator is not zero.

Finding the Square Root of 981

The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, we use methods like the long division method and the approximation method. Let us explore these methods:

  1. Prime factorization method 
  2. Long division method 
  3. Approximation method

Square Root of 981 by Prime Factorization Method

Prime factorization involves expressing a number as the product of its prime factors. Let us break down 981 into its prime factors:

Step 1: Finding the prime factors of 981 Breaking it down, we get 3 x 3 x 109: 3^2 x 109^1

Step 2: Now that we have found the prime factors of 981, we attempt to form pairs of prime factors. Since 981 is not a perfect square, the digits of the number cannot be grouped into pairs, making it impossible to calculate √981 using prime factorization directly.

Explore Our Programs

Square Root of 981 by Long Division Method

The long division method is particularly useful for non-perfect square numbers. This method involves finding a series of approximations to reach the square root. Here is how you can find the square root using the long division method, step by step:

Step 1: Group the digits of the number in pairs from right to left. For 981, we group it as 9 and 81.

Step 2: Find n such that n2 is less than or equal to 9. Here, n is 3 because 3 x 3 = 9. Subtract 9 from 9, and the remainder is 0.

Step 3: Bring down the next pair of digits, 81, making the new dividend 81. Double the quotient obtained in the previous step (3), giving a new divisor of 6.

Step 4: Find a digit x such that 6x multiplied by x is less than or equal to 81. Here x is 1 because 61 x 1 = 61. Subtract 61 from 81 to get a remainder of 20.

Step 5: Bring down two zeros to make the dividend 2000. Double the quotient (31), making the new divisor 62.

Step 6: Find a digit y such that 62y x y is less than or equal to 2000. Here y is 3 because 623 x 3 = 1869. Subtract 1869 from 2000 to get a remainder of 131.

Step 7: Repeat the process to obtain more decimal places.

The quotient so far is 31.32. So the square root of √981 is approximately 31.32.

Square Root of 981 by Approximation Method

The approximation method is an easy way to estimate the square roots of numbers. Here's how to approximate the square root of 981:

Step 1: Find the closest perfect squares around 981. The closest perfect squares are 961 (312) and 1024 (322). √981 falls between 31 and 32.

Step 2: Apply the formula: (Given number - smaller perfect square) / (Larger perfect square - smaller perfect square). (981 - 961) / (1024 - 961) = 20 / 63 ≈ 0.317

Using the formula, the approximate decimal part is 0.317. Adding this to the integer part gives us 31 + 0.317 ≈ 31.317.

Thus, the square root of 981 is approximately 31.317.

Common Mistakes and How to Avoid Them in the Square Root of 981

Students often make mistakes when finding square roots, such as forgetting about the negative square root or skipping steps in the long division method. Let's look at some common mistakes in detail.

Download Worksheets

Problem 1

Can you help Max find the area of a square box if its side length is given as √981?

Okay, lets begin

The area of the square is approximately 981 square units.

Explanation

The area of a square is given by side2.

If the side length is √981, then the area is (√981)² = 981.

Therefore, the area of the square box is approximately 981 square units.

Well explained 👍

Problem 2

A square-shaped garden measuring 981 square feet is built; if each side is √981, what will be the area of half of the garden?

Okay, lets begin

490.5 square feet

Explanation

Since the garden is square-shaped, its area is evenly divided.

Dividing 981 by 2 gives 490.5,

so half of the garden measures 490.5 square feet.

Well explained 👍

Problem 3

Calculate √981 x 5.

Okay, lets begin

Approximately 156.6

Explanation

First, find the square root of 981, which is approximately 31.32.

Then multiply 31.32 by 5 to get approximately 156.6.

Well explained 👍

Problem 4

What will be the square root of (961 + 20)?

Okay, lets begin

The square root is approximately 31.32

Explanation

First, find the sum of 961 + 20, which is 981

. Then find the square root of 981, which is approximately 31.32.

Therefore, the square root of (961 + 20) is approximately 31.32.

Well explained 👍

Problem 5

Find the perimeter of a rectangle if its length ‘l’ is √981 units and the width ‘w’ is 40 units.

Okay, lets begin

The perimeter of the rectangle is approximately 142.64 units.

Explanation

Perimeter of a rectangle = 2 × (length + width)

Perimeter = 2 × (√981 + 40)

= 2 × (31.32 + 40) ≈ 2 × 71.32 ≈ 142.64 units.

Well explained 👍

FAQ on Square Root of 981

1.What is √981 in its simplest form?

The prime factorization of 981 is 3 x 3 x 109, so the simplest form of √981 = √(3 x 3 x 109) = 3√109.

2.What are the factors of 981?

Factors of 981 are 1, 3, 9, 27, 37, 111, 333, and 981.

3.Calculate the square of 981.

The square of 981 is 961,461, calculated as 981 x 981.

4.Is 981 a prime number?

No, 981 is not a prime number as it has more than two factors.

5.What numbers is 981 divisible by?

981 is divisible by 1, 3, 9, 27, 37, 111, 333, and itself, 981.

Important Glossaries for the Square Root of 981

  • Square root: The square root of a number is a value that, when multiplied by itself, gives the original number. Example: 42 = 16, so the square root of 16 is √16 = 4.
  • Irrational number: A number that cannot be expressed as a simple fraction, with a non-repeating, non-terminating decimal expansion.
  • Long division method: A step-by-step process used to find the square root of a non-perfect square by dividing and averaging.
  • Approximation: An approach to estimating a number or value, often used when an exact calculation is not possible or necessary.
  • Perfect square: A number that is the square of an integer. For example, 16 is a perfect square because it is 42.

What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math

▶

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.