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Last updated on May 26th, 2025

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Square Root of 8/9

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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 various fields such as engineering, finance, etc. Here, we will discuss the square root of 8/9.

Square Root of 8/9 for Australian Students
Professor Greenline from BrightChamps

What is the Square Root of 8/9?

The square root is the inverse of the square of a number. 8/9 is a fraction, and its square root can be expressed in both radical and exponential forms. In radical form, it is expressed as √(8/9), whereas in exponential form, it is (8/9)^(1/2). The square root of 8/9 simplifies to √8/√9, which is approximately 0.94281. This is a rational number because it can be expressed as a fraction.

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Finding the Square Root of 8/9

To find the square root of a fraction, you can take the square root of the numerator and the square root of the denominator separately. Let us now learn the following methods: Simplification method Decimal approximation method

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Square Root of 8/9 by Simplification Method

To simplify the square root of a fraction like 8/9, follow these steps:

 

Step 1: Find the square root of the numerator and the denominator separately. The numerator is 8, and the denominator is 9.

 

Step 2: The square root of 8 is approximately 2.82843, and the square root of 9 is exactly 3.

 

Step 3: Divide the square root of the numerator by the square root of the denominator: 2.82843/3 = 0.94281.

 

Thus, the square root of 8/9 is approximately 0.94281.

Professor Greenline from BrightChamps

Square Root of 8/9 by Decimal Approximation Method

The decimal approximation method for finding the square root is straightforward. Here is how you can find the square root of 8/9 using this method:

 

Step 1: Convert the fraction 8/9 into a decimal, which is approximately 0.88889.

 

Step 2: Use a calculator to find the square root of 0.88889, which is approximately 0.94281.

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Common Mistakes and How to Avoid Them in the Square Root of 8/9

Students often make mistakes while finding the square root, such as forgetting to simplify the fraction or incorrectly applying the square root to both the numerator and the denominator separately. Here are some common mistakes and how to avoid them.

Mistake 1

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Forgetting to Simplify the Fraction

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It is crucial to simplify the fraction before finding its square root when possible. For example, if the fraction can be reduced, do so before taking the square root. Simplification can lead to easier calculations and more accurate results.

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Square Root of 8/9 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 √(8/9)?

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The area of the square is 0.88889 square units.

Explanation

The area of the square = side².

The side length is given as √(8/9).

Area of the square = (√(8/9))²

= 8/9

= 0.88889.

Therefore, the area of the square box is 0.88889 square units.

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Max, the Girl Character from BrightChamps

Problem 2

A square-shaped building measuring 8/9 square feet is built; if each of the sides is √(8/9), what will be the square feet of half of the building?

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0.44444 square feet

Explanation

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

Dividing 8/9 by 2 = (8/9)/2

= 0.44444.

So half of the building measures 0.44444 square feet.

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Max, the Girl Character from BrightChamps

Problem 3

Calculate √(8/9) x 5.

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4.71405

Explanation

The first step is to find the square root of 8/9, which is approximately 0.94281.

The second step is to multiply 0.94281 by 5. So 0.94281 x 5 = 4.71405.

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Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (8/9 + 1/9)?

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The square root is 1.

Explanation

To find the square root, first find the sum of (8/9 + 1/9).

8/9 + 1/9 = 9/9 = 1, and then √1 = 1.

Therefore, the square root of (8/9 + 1/9) is 1.

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Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of the rectangle if its length 'l' is √(8/9) units and the width 'w' is 1 unit.

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The perimeter of the rectangle is 3.88562 units.

Explanation

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

Perimeter = 2 × (√(8/9) + 1)

= 2 × (0.94281 + 1)

= 2 × 1.94281

= 3.88562 units.

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FAQ on Square Root of 8/9

1.What is √(8/9) in its simplest form?

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2.Can the square root of 8/9 be expressed as a fraction?

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3.Calculate the square of 8/9.

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4.Is 8/9 a perfect square?

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5.What are the factors of 8/9?

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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 8/9?

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8.How do technology and digital tools in Australia support learning Algebra and Square Root of 8/9?

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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 8/9

  • Square root: A square root is the inverse of a square. For example, 3² = 9, and the inverse of the square is the square root, so √9 = 3.
     
  • Rational number: A rational number is a number that can be expressed in the form p/q, where q is not equal to zero and p and q are integers.
     
  • Fraction: A fraction represents a part of a whole or any number of equal parts. It is expressed as a/b, where a is the numerator and b is the denominator.
     
  • Decimal: A decimal is a way of expressing numbers that include a whole number and a fraction, represented with a decimal point. For example, 0.5, 0.75, and 1.25 are decimals. 
     
  • Perfect square: A perfect square is a number that is the square of an integer. For example, 9 is a perfect square because it is 3².
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 8/9 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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