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Last updated on May 26th, 2025

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Square Root of 1/961

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If a number is multiplied by itself, the result is a square. The inverse operation is the square root. The square root is used in various fields such as vehicle design, finance, etc. Here, we will discuss the square root of 1/961.

Square Root of 1/961 for Australian Students
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What is the Square Root of 1/961?

The square root is the inverse of squaring a number. 1/961 is a fraction and can be considered a perfect square. The square root of 1/961 is expressed in both radical and exponential forms. In radical form, it is expressed as √(1/961), whereas in exponential form, it is (1/961)^(1/2). The square root of 1/961 is 1/31, which is a rational number because it can be expressed in the form of p/q, where p and q are integers and q ≠ 0.

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Finding the Square Root of 1/961

The prime factorization method can be used for perfect squares, and since 1/961 can be broken down into perfect squares, it can be simplified easily. Let's learn the following methods:

 

  • Prime factorization method
     
  • Direct calculation
Professor Greenline from BrightChamps

Square Root of 1/961 by Prime Factorization Method

Prime factorization involves expressing a number as the product of its prime factors. Let's break down 961:

 

Step 1: Prime factorization of 961 Breaking it down, we get 31 x 31: 31^2

 

Step 2: Since 1/961 is 1/(31^2), the square root is 1/31. This is because the square root of a quotient is the quotient of the square roots.

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Square Root of 1/961 by Direct Calculation

For fractions like 1/961, the square root can be calculated directly:

 

Step 1: Recognize that 961 = 31^2.

 

Step 2: The square root of 1 is 1.

 

Step 3: Therefore, the square root of 1/961 is 1/31.

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Square Root of 1/961 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 √(1/961)?

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The area of the square is 1/961 square units.

Explanation

The area of a square = side². Since the side length is √(1/961), the area is (√(1/961))² = 1/961. Therefore, the area is 1/961 square units.

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Max, the Girl Character from BrightChamps

Problem 2

A square-shaped garden measures 1/961 square feet; if each of the sides is √(1/961), what will be the square feet of half of the garden?

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1/1922 square feet

Explanation

To find half of the area, simply divide the total area by 2. (1/961) ÷ 2 = 1/1922. Therefore, half of the garden measures 1/1922 square feet.

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Problem 3

Calculate √(1/961) x 5.

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5/31

Explanation

First, find the square root of 1/961, which is 1/31. Then multiply 1/31 by 5. (1/31) x 5 = 5/31.

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Problem 4

What will be the square root of (1/961 + 1)?

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Approximately 1.032

Explanation

First, find the sum: 1/961 + 1 = 962/961 Then find the square root: √(962/961) ≈ 1.032

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Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √(1/961) units and the width ‘w’ is 38 units.

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76.064516 units

Explanation

Perimeter of the rectangle = 2 × (length + width) Perimeter = 2 × (1/31 + 38) = 2 × (0.032258 + 38) = 2 × 38.032258 = 76.064516 units.

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FAQ on Square Root of 1/961

1.What is √(1/961) in its simplest form?

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2.Mention the factors of 961.

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3.Calculate the square of 1/961.

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4.Is 961 a prime number?

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5.961 is divisible by?

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

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7.How can cultural or local activities in Australia support learning Algebra topics such as Square Root of 1/961?

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8.How do technology and digital tools in Australia support learning Algebra and Square Root of 1/961?

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

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Professor Greenline from BrightChamps

Important Glossaries for the Square Root of 1/961

  • Square root: A square root is the inverse of squaring a number. For example, 5² = 25, and the inverse is √25 = 5.

 

  • Rational number: A rational number can be expressed in the form of p/q, where p and q are integers and q ≠ 0.

 

  • Perfect square: A perfect square is a number that can be expressed as the square of an integer. For example, 961 is a perfect square (31²).

 

  • Fraction: A fraction represents a part of a whole and is expressed as a ratio of two numbers, such as 1/31.

 

  • Quotient: In division, the quotient is the result of dividing one number by another. For example, in 10 ÷ 2 = 5, the quotient is 5.
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About BrightChamps in Australia

At BrightChamps, we believe algebra is more than symbols—it opens doors to endless opportunities! Our mission is to help children all over Australia gain important math skills, focusing today on the Square Root of 1/961 with a special emphasis on understanding square roots—in a lively, fun, and easy-to-grasp way. Whether your child is calculating the speed of a roller coaster at Luna Park Sydney, tracking cricket match scores, or managing their allowance for the newest gadgets, mastering algebra gives them the confidence to tackle everyday problems. Our interactive lessons make learning both simple and enjoyable. Since children in Australia learn in various ways, we adapt our approach to fit each learner’s style. From Sydney’s vibrant streets to the stunning Gold Coast beaches, BrightChamps brings math to life, making it relevant and exciting throughout Australia. Let’s make square roots a joyful 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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Fun Fact

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

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