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Last updated on May 26th, 2025

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Square Root of 64/121

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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 64/121.

Square Root of 64/121 for Australian Students
Professor Greenline from BrightChamps

What is the Square Root of 64/121?

The square root is the inverse of the square of the number. The fraction 64/121 can be expressed as a perfect square. The square root of 64/121 is expressed in both radical and exponential forms. In radical form, it is expressed as √(64/121), whereas (64/121)^(1/2) is in the exponential form. √(64/121) = 8/11, 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 64/121

The prime factorization method is used for perfect square numbers. Since 64/121 is a perfect square, we can use prime factorization, along with other methods if necessary. Let us now learn the following methods:

 

  • Prime factorization method
  • Simplification method
  • Verification method
Professor Greenline from BrightChamps

Square Root of 64/121 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 64 and 121 are broken down into their prime factors.

 

Step 1: Finding the prime factors of 64 and 121.

 

  • 64 can be broken down as 2 x 2 x 2 x 2 x 2 x 2 (i.e., 2^6). 
  • 121 can be broken down as 11 x 11 (i.e., 11^2).

 

Step 2: Now that we found the prime factors, we can take the square root of each part. √(64/121) = √(2^6)/√(11^2) = (2^3)/(11) = 8/11.

Professor Greenline from BrightChamps

Square Root of 64/121 by Simplification Method

The simplification method is a straightforward way to find the square root of a fraction if both numerator and denominator are perfect squares.

 

Step 1: Identify the square roots of the numerator and the denominator separately. 

 

  • The square root of 64 is 8. 
  • The square root of 121 is 11.

 

Step 2: Divide the square root of the numerator by the square root of the denominator.

 

So, √(64/121) = 8/11.

Professor Greenline from BrightChamps

Verification of the Square Root of 64/121

Verification is another way to ensure that the calculation is correct.

 

Step 1: Multiply the result by itself to see if it equals the original fraction. (8/11) x (8/11) = 64/121.

 

Step 2: Since this equals the original fraction, the square root calculation is verified.

Max Pointing Out Common Math Mistakes

Common Mistakes and How to Avoid Them in the Square Root of 64/121

Students make mistakes while finding the square root, such as misunderstanding fractions and skipping steps in simplification. 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: √(64/121) = ±8/11, but we typically use the positive value.

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Square Root of 64/121 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 √(64/121)?

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The area of the square is 64/121 square units.

Explanation

The area of the square = side^2.

The side length is given as √(64/121).

Area of the square = side^2 = (8/11) x (8/11) = 64/121.

Therefore, the area of the square box is 64/121 square units.

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Max, the Girl Character from BrightChamps

Problem 2

A square-shaped building measuring 64/121 square feet is built; if each of the sides is √(64/121), what will be the square feet of half of the building?

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32/121 square feet

Explanation

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

Dividing 64/121 by 2 = 32/121.

So half of the building measures 32/121 square feet.

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Max, the Girl Character from BrightChamps

Problem 3

Calculate √(64/121) x 5.

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40/11

Explanation

The first step is to find the square root of 64/121, which is 8/11, the second step is to multiply 8/11 by 5.

So, (8/11) x 5 = 40/11.

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Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (64/121 + 1)?

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The square root is 12/11.

Explanation

To find the square root, we need to find the sum of (64/121 + 1). 64/121 + 121/121 = 185/121.

Now, √(185/121) = √185/√121 = √185/11.

Since 185 is not a perfect square, we approximate it.

The approximate square root is around 12/11.

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 √(64/121) units and the width ‘w’ is 3 units.

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

We find the perimeter of the rectangle as 70/11 units.

Explanation

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

Perimeter = 2 × (8/11 + 3) = 2 × (8/11 + 33/11) = 2 × 41/11 = 82/11 = 70/11 units.

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FAQ on Square Root of 64/121

1.What is √(64/121) in its simplest form?

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2.Mention the factors of 64 and 121.

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3.Calculate the square of 64/121.

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4.Is 64/121 a rational number?

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5.Is 64/121 a perfect square?

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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 64/121?

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8.How do technology and digital tools in Australia support learning Algebra and Square Root of 64/121?

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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 64/121

  • Square root: A square root is the inverse of a square. Example: 4^2 = 16, and the inverse of the square is the square root, that is, √16 = 4.

 

  • Rational number: A rational number is a number that can be written in the form of p/q, where q is not equal to zero, and p and q are integers.

 

  • Perfect square: A number that is the square of an integer. Example: 64 and 121 are perfect squares.

 

  • Fraction: A way to represent numbers that are not whole, using a numerator and a denominator. Example: 64/121 is a fraction.

 

  • Prime factorization: The process of expressing a number as the product of its prime factors. Example: 64 = 2^6.
Professor Greenline from BrightChamps

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 64/121 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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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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