Square Root of 984
2026-02-28 17:51 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-984

320 Learners

Last updated on August 5, 2025

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.

What is the Square Root of 984?

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

Finding the Square Root of 984

The prime factorization method works well for perfect squares. For non-perfect squares like 984, other methods such as the long division method and approximation method are used. Let's explore these methods: -

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

Square Root of 984 by Prime Factorization Method

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

Step 1: 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

Step 2: 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.

Explore Our Programs

Square Root of 984 by Long Division Method

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

Step 1: Group the number from right to left. For 984, we group it as 98 and 4.

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

Step 3: Bring down the next pair, 4, making the new dividend 174. Add the last divisor (9) to itself, making it 18.

Step 4: 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.

Step 5: Subtract 1701 from 1744, resulting in 43.

Step 6: Since the remainder is less than the divisor, add a decimal point and continue the process.

Step 7: Continue these steps until the desired decimal accuracy is reached. The square root of 984 is approximately 31.368.

Square Root of 984 by Approximation Method

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

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

Step 2: 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

Thus, √984 is approximately 31.365.

Common Mistakes and How to Avoid Them in the Square Root of 984

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:

Download Worksheets

Problem 1

If a square has a side length of √984, what is its area?

Okay, lets begin

The area of the square is approximately 984 square units.

Explanation

The area of a square is calculated as side².

If the side length is √984, then the area is (√984)² = 984 square units.

Well explained 👍

Problem 2

A garden has an area of 984 square feet. What is the length of one side of the garden?

Okay, lets begin

The side length of the garden is approximately 31.368 feet.

Explanation

The side length of the garden is the square root of the area.

Thus, the side length is √984 ≈ 31.368 feet.

Well explained 👍

Problem 3

Calculate 5 times the square root of 984.

Okay, lets begin

The result is approximately 156.84.

Explanation

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

Well explained 👍

Problem 4

What is the square root of (984 + 16)?

Okay, lets begin

The square root is approximately 32.

Explanation

Calculate the sum: 984 + 16 = 1000.

Then find the square root: √1000 ≈ 31.622.

However, considering approximation, it is often rounded to 32 for practical purposes.

Well explained 👍

Problem 5

Find the perimeter of a rectangle with length √984 units and width 40 units.

Okay, lets begin

The perimeter is approximately 142.736 units.

Explanation

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

Length = √984 ≈ 31.368.

Therefore, the perimeter = 2 × (31.368 + 40) = 2 × 71.368 = 142.736 units.

Well explained 👍

FAQ on Square Root of 984

1.What is √984 in its simplest form?

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

2.What are the factors of 984?

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

3.Calculate the square of 984.

The square of 984 is 984 × 984 = 968,256.

4.Is 984 a prime number?

5.Which numbers is 984 divisible by?

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

Important Glossaries for the Square Root of 984

  • - Square root: 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. -
  • Irrational number: A number that cannot be written as a simple fraction; its decimal form is non-terminating and non-repeating. Example: √2. -
  • Prime factorization: The expression of a number as a product of its prime numbers. -
  • Perfect square: A number that is the square of an integer. Example: 49, because 7 × 7 = 49. -
  • Long division method: A step-by-step process of dividing numbers to find the square root of non-perfect squares.

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.