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Last updated on May 26th, 2025

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Square Root of 968

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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 968.

Square Root of 968 for Qatari Students
Professor Greenline from BrightChamps

What is the Square Root of 968?

The square root is the inverse of the square of the number. 968 is not a perfect square. The square root of 968 is expressed in both radical and exponential forms. In the radical form, it is expressed as √968, whereas (968)(1/2) in the exponential form. √968 ≈ 31.1, 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.

Professor Greenline from BrightChamps

Finding the Square Root of 968

The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where the long-division method and approximation method are used. Let us now learn the following methods:

 

  1. Prime factorization method
  2. Long division method
  3. Approximation method
Professor Greenline from BrightChamps

Square Root of 968 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 968 is broken down into its prime factors.

 

Step 1: Finding the prime factors of 968 Breaking it down, we get 2 × 2 × 2 × 11 × 11: 23 × 112

 

Step 2: Now that we have found the prime factors of 968, the second step is to make pairs of those prime factors. Since 968 is not a perfect square, therefore the digits of the number can’t be grouped in complete pairs.

 

Therefore, calculating the exact square root of 968 using prime factorization alone is not possible.

Professor Greenline from BrightChamps

Square Root of 968 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, we need to group the numbers from right to left. In the case of 968, we can consider it as 9 and 68.

 

Step 2: Now we need to find n whose square is less than or equal to 9. We can say n is ‘3’ because 3 × 3 is 9. Now the quotient is 3, and the remainder is 0.

 

Step 3: Now bring down 68, which is the new dividend. Add the old divisor (3) with the same number to get 6, which will be part of our new divisor.

 

Step 4: We double the quotient (3) and consider the next digit we need. The new divisor will be 6n.

 

Step 5: The next step is finding 6n × n ≤ 68; let us consider n as 1, now 6 × 1 × 1 = 6. Step 6: Subtract 68 from 6; the difference is 62.

 

Step 7: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 6200.

 

Step 8: Now we need to find the new digit n for the divisor 61n. Choose n = 1.

 

Step 9: Subtract the product from the dividend and continue the process until you obtain a precise value.

 

So, the square root of √968 is approximately 31.1.

Professor Greenline from BrightChamps

Square Root of 968 by Approximation Method

The approximation method is another method for finding the square roots. It is an easy method to find the square root of a given number. Now let us learn how to find the square root of 968 using the approximation method.

 

Step 1: Now we have to find the closest perfect squares around √968. The closest perfect squares to 968 are 961 (312) and 1024 (322). √968 falls somewhere between 31 and 32.

 

Step 2: Now we need to apply a formula for approximation. Using the approximation formula, we can determine a more accurate value between the two perfect squares.

 

Using interpolation or an approximation formula, we find that √968 is approximately 31.1.

Max Pointing Out Common Math Mistakes

Common Mistakes and How to Avoid Them in the Square Root of 968

Students do make mistakes while finding the square root, like forgetting about the negative square root or skipping long division steps. Now let us look at a few of those mistakes that students tend to make in detail.

Mistake 1

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Forgetting about the negative square root

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It is important to make students aware that a number does have both positive and negative square roots. However, we will be taking only the positive square root, as it is the required one. For example: √50 = 7.07, there is also -7.07, which should not be forgotten.

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Square Root of 968 Examples

Ray, the Character from BrightChamps Explaining Math Concepts
Max, the Girl Character from BrightChamps

Problem 1

Can you help Max find the area of a square box if its side length is given as √968?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

The area of the square is approximately 936.1 square units.

Explanation

The area of the square = side2.

 

The side length is given as √968.

 

Area of the square = side2 = √968 × √968 = 968.

 

Therefore, the area of the square box is approximately 968 square units.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 2

A square-shaped building measuring 968 square feet is built; if each of the sides is √968, what will be the square feet of half of the building?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

484 square feet

Explanation

We can just divide the given area by 2 as the building is square-shaped.

 

Dividing 968 by 2, we get 484.

 

So half of the building measures 484 square feet.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 3

Calculate √968 × 5.

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

Approximately 155.5

Explanation

The first step is to find the square root of 968, which is approximately 31.1.

 

The second step is to multiply 31.1 with 5.

 

So 31.1 × 5 ≈ 155.5.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (948 + 20)?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

The square root is 32.

Explanation

To find the square root,

 

we need to find the sum of (948 + 20). 948 + 20 = 968, and then √968 ≈ 31.1.

 

Therefore, the square root of (948 + 20) is approximately ±31.1.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √968 units and the width ‘w’ is 38 units.

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

We find the perimeter of the rectangle as approximately 140.2 units.

Explanation

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

 

Perimeter = 2 × (√968 + 38) ≈ 2 × (31.1 + 38) ≈ 2 × 69.1 ≈ 138.2 units.

Max from BrightChamps Praising Clear Math Explanations
Ray Thinking Deeply About Math Problems

FAQ on Square Root of 968

1.What is √968 in its simplest form?

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2.Mention the factors of 968.

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3.Calculate the square of 968.

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4.Is 968 a prime number?

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5.968 is divisible by?

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6.How does learning Algebra help students in Qatar make better decisions in daily life?

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7.How can cultural or local activities in Qatar support learning Algebra topics such as Square Root of 968?

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8.How do technology and digital tools in Qatar support learning Algebra and Square Root of 968?

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9.Does learning Algebra support future career opportunities for students in Qatar?

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Professor Greenline from BrightChamps

Important Glossaries for the Square Root of 968

  • Square root: A square root is the inverse operation of squaring a number. Example: 42 = 16, and the inverse of squaring is the square root, so √16 = 4.

 

  • Irrational number: An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.

 

  • Long division method: A method used to find the square root of non-perfect squares, involving division and subtraction in repeated steps to approximate the root.

 

  • Perfect square: A number that is the square of an integer. Example: 49 is a perfect square because it is 72.

 

  • Approximation method: A technique for estimating the value of a square root by finding two consecutive perfect squares and interpolating between them.
Professor Greenline from BrightChamps

About BrightChamps in Qatar

At BrightChamps, we know algebra is more than just symbols—it opens doors to many possibilities! Our aim is to support children all over Qatar in mastering key math skills, focusing today on the Square Root of 968 with a special focus on square roots—in a lively, engaging, and easy-to-understand way. Whether your child is calculating the speed of a roller coaster at Qatar’s Angry Birds World, tracking scores at local football matches, or managing their allowance for the latest gadgets, mastering algebra builds their confidence to face everyday challenges. Our interactive lessons make learning both fun and simple. Since kids in Qatar learn in various ways, we tailor our approach to each learner. From Doha’s modern cityscape to desert landscapes, BrightChamps makes math relatable and exciting throughout Qatar. Let’s make square roots a fun part of every child’s math journey!
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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.

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Max, the Girl Character from BrightChamps

Fun Fact

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

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