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Last updated on May 26th, 2025

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Square Root of 962

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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 is used in fields such as architecture, finance, and engineering. Here, we will discuss the square root of 962.

Square Root of 962 for UK Students
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What is the Square Root of 962?

The square root is the inverse operation of squaring a number. The number 962 is not a perfect square. The square root of 962 is expressed in both radical and exponential form. In radical form, it is expressed as √962, whereas in exponential form it is written as 962(1/2). The square root of 962 is approximately 31.014, which is an irrational number because it cannot be expressed as a fraction p/q, where p and q are integers and q ≠ 0.

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Finding the Square Root of 962

The prime factorization method is typically used for perfect square numbers. However, for non-perfect squares like 962, the long division method and approximation method are more suitable. Let us explore these methods: -

 

  1. Long division method 
  2. Approximation method
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Square Root of 962 by Long Division Method

The long division method is particularly useful for finding the square root of non-perfect square numbers. Here is how you can find the square root of 962 using the long division method, step by step:

 

Step 1: Begin by pairing the digits of 962 from right to left, which gives us 62 and 9.

 

Step 2: Find the largest number whose square is less than or equal to 9. That number is 3 because 3 × 3 = 9. Subtract 9 from 9, leaving a remainder of 0.

 

Step 3: Bring down the next pair, which is 62, making the new dividend 62.

 

Step 4: Double the divisor (3) to get 6, which becomes the new divisor prefix. Now, determine a digit n such that 6n × n is less than or equal to 62.

 

Step 5: The largest n satisfying this condition is 1, since 61 × 1 = 61. Subtract 61 from 62 to get a remainder of 1.

 

Step 6: Add a decimal point to the quotient and bring down two zeros to make the new dividend 100.

 

Step 7: Double the current quotient (31) to get 62. Find a digit n such that 62n × n is less than or equal to 100.

 

Step 8: The largest n is 1, since 621 × 1 = 621. Subtract 621 from 1000 to get a remainder of 379.

 

Step 9: Continue this process until you achieve the desired accuracy. The square root of 962 is approximately 31.014.

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Square Root of 962 by Approximation Method

The approximation method provides a quick and easy way to estimate the square root of a number. Here's how to find the square root of 962 using this method:

 

Step 1: Identify the perfect squares nearest to 962. The perfect squares are 961 (31²) and 1024 (32²). Thus, √962 is between 31 and 32.

 

Step 2: Use the formula: (Given number - smaller perfect square) / (Larger perfect square - smaller perfect square). Using this formula: (962 - 961) / (1024 - 961) = 1/63 ≈ 0.0159.

 

Adding this to 31 gives approximately 31.0159, so √962 ≈ 31.014.

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Common Mistakes and How to Avoid Them in the Square Root of 962

Students often make mistakes when finding square roots, such as forgetting about negative roots or misapplying methods. Here are some common mistakes and how to avoid them.

Mistake 1

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Forgetting about the Negative Square Root

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It is important to remember that every positive number has both a positive and a negative square root. However, in most practical applications, only the positive root is used. For example, √50 = 7.07, but there is also -7.07.

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Square Root of 962 Examples

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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 √962?

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The area of the square is approximately 924.868 square units.

Explanation

The area of a square is calculated as side².

 

Given the side length as √962, the area = (√962)² = 962.

 

Therefore, the area of the square box is approximately 924.868 square units when rounded.

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Problem 2

A square-shaped garden measuring 962 square feet is built. If each side is √962, what will be the square feet of half of the garden?

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481 square feet

Explanation

To find half the area of the square, divide the total area by 2.

 

So, 962 ÷ 2 = 481.

 

Therefore, half of the garden measures 481 square feet.

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Problem 3

Calculate √962 × 5.

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Approximately 155.07

Explanation

First, find the square root of 962, which is approximately 31.014.

 

Then multiply 31.014 by 5.

 

So, 31.014 × 5 ≈ 155.07.

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Problem 4

What will be the square root of (962 - 2)?

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The square root is approximately 31.

Explanation

First, find the difference: 962 - 2 = 960. Then find the square root of 960, which is approximately 31.

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Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of a rectangle if its length ‘l’ is √962 units and the width ‘w’ is 38 units.

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The perimeter of the rectangle is approximately 138.028 units.

Explanation

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

 

Given length = √962 and width = 38:

 

Perimeter = 2 × (31.014 + 38)

 

= 2 × 69.014 = 138.028 units.

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FAQ on Square Root of 962

1.What is √962 in its simplest form?

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2.What are the factors of 962?

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3.Calculate the square of 962.

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4.Is 962 a prime number?

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5.962 is divisible by?

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

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7.How can cultural or local activities in United Kingdom support learning Algebra topics such as Square Root of 962?

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8.How do technology and digital tools in United Kingdom support learning Algebra and Square Root of 962?

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

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Important Glossaries for the Square Root of 962

  • Square root: The square root of a number is a value that, when multiplied by itself, gives the original number. Example: √16 = 4.

 

  • Irrational number: A number that cannot be written as a simple fraction; its decimal form is non-repeating and non-terminating. Example: π, √2.

 

  • Radical: The symbol (√) used to denote the root of a number. For example, √25 = 5.

 

  • Approximation: A value or number that is close to but not exactly equal to another number; often used when dealing with irrational numbers.

 

  • Long division method: A step-by-step process for dividing multi-digit numbers, often used to find square roots of non-perfect squares.
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About BrightChamps in United Kingdom

At BrightChamps, we believe algebra goes beyond symbols—it unlocks countless opportunities! Our mission is to help children throughout the United Kingdom develop essential math skills, focusing today on the Square Root of 962 with an emphasis on understanding square roots—in a lively, enjoyable, and straightforward way. Whether your child is figuring out the speed of a roller coaster at Alton Towers, tallying scores at a local football match, or managing their pocket money for the newest gadgets, mastering algebra gives them the confidence for everyday challenges. Our interactive lessons keep learning simple and enjoyable. Because children in the UK learn differently, we adapt our approach to fit each child’s unique needs. From the bustling streets of London to the scenic Cornish coasts, BrightChamps makes math relatable and exciting throughout the UK. Let’s bring square roots into 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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Fun Fact

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

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