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Last updated on May 26th, 2025

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Square Root of 25/9

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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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 25/9.

Square Root of 25/9 for Indonesian Students
Professor Greenline from BrightChamps

What is the Square Root of 25/9?

The square root is the inverse of the square of the number. 25/9 is a perfect square fraction. The square root of 25/9 is expressed in both radical and exponential form. In the radical form, it is expressed as √(25/9), whereas (25/9)^(1/2) in the exponential form. √(25/9) = 5/3, 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.

Professor Greenline from BrightChamps

Finding the Square Root of 25/9

The prime factorization method is used for perfect square numbers. However, for perfect square fractions like 25/9, we can find the square root by taking the square root of both the numerator and the denominator separately. Let us now learn the following methods: 

 

  • Prime factorization method 
  • Simplification method
Professor Greenline from BrightChamps

Square Root of 25/9 by Prime Factorization Method

The product of prime factors is the Prime factorization of a number. Now let us look at how 25 and 9 are broken down into their prime factors:

 

Step 1: Finding the prime factors of 25 and 9 - 25 can be broken down as 5 x 5: 5² - 9 can be broken down as 3 x 3: 3²

 

Step 2: Since both 25 and 9 are perfect squares, we can easily find the square root of each.

 

Thus, √(25/9) = √25/√9 = 5/3.

Professor Greenline from BrightChamps

Square Root of 25/9 by Simplification Method

The simplification method involves simplifying the given fraction and then finding the square root.

 

Step 1: The fraction 25/9 is already in its simplest form.

 

Step 2: Find the square root of the numerator and the denominator separately: √25 = 5 and √9 = 3.

 

Step 3: Therefore, √(25/9) = 5/3.

Max Pointing Out Common Math Mistakes

Common Mistakes and How to Avoid Them in the Square Root of 25/9

Students do make mistakes while finding the square root, such as forgetting about the negative square root or confusing square roots with cube roots. 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 typically consider only the positive square root, as it is the principal root.

For example, √(25/9) = 5/3, but there is also -5/3.

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Square Root of 25/9 Examples

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

Problem 1

Can you help Max find the side length of a square box if its area is given as 25/9 square units?

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

The side length of the square is 5/3 units.

Explanation

The side length of the square = √(area).

The area is given as 25/9 square units.

Side length of the square = √(25/9)

= 5/3 units.

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Max, the Girl Character from BrightChamps

Problem 2

A rectangular garden has an area of 25/9 square meters. If the width is 1/3 meters, what is the length?

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

The length of the garden is 5 meters.

Explanation

Area of the rectangle = length × width.

Given the area is 25/9 and the width is 1/3 meters.

Length = (Area/Width)

= (25/9) ÷ (1/3)

= (25/9) × (3/1)

= 25/3

= 5 meters.

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

Problem 3

Calculate √(25/9) × 4.

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

20/3

Explanation

The first step is to find the square root of 25/9, which is 5/3.

The second step is to multiply 5/3 by 4.

So, (5/3) × 4 = 20/3.

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

Problem 4

What will be the square root of (16 + 9)?

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

The square root is 5.

Explanation

To find the square root, we need to find the sum of (16 + 9).

16 + 9 = 25, and then √25 = 5.

Therefore, the square root of (16 + 9) is ±5.

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

Problem 5

Find the perimeter of a rectangle if its length 'l' is √(25/9) units and the width 'w' is 3 units.

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

The perimeter of the rectangle is 16 units.

Explanation

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

Perimeter = 2 × (√(25/9) + 3)

= 2 × (5/3 + 3)

= 2 × (5/3 + 9/3)

= 2 × 14/3

= 28/3

= 16 units.

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

FAQ on Square Root of 25/9

1.What is √(25/9) in its simplest form?

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2.Mention the factors of 25/9.

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3.Calculate the square of 25/9.

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4.Is 25/9 a prime fraction?

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5.25/9 is divisible by?

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

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7.How can cultural or local activities in Indonesia support learning Algebra topics such as Square Root of 25/9?

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8.How do technology and digital tools in Indonesia support learning Algebra and Square Root of 25/9?

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

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Professor Greenline from BrightChamps

Important Glossaries for the Square Root of 25/9

  • Square root: A square root is the inverse operation to squaring a number. For example, 4² = 16, and the inverse of the square is the square root, √16 = 4.
     
  • Rational number: A rational number is a number that can be written in the form of p/q, where p and q are integers and q is not equal to zero.
     
  • Principal square root: The principal square root is the positive square root of a number. For example, the principal square root of 9 is 3.
     
  • Perfect square: A perfect square is a number that can be expressed as the square of an integer. For example, 25 is a perfect square because it is 5².
     
  • Fraction: A fraction is a numerical quantity that is not a whole number, representing a part of a whole. It is expressed as a ratio of two numbers, such as 5/3.
Professor Greenline from BrightChamps

About BrightChamps in Indonesia

At BrightChamps, we believe algebra is more than symbols—it’s a doorway to endless possibilities! We aim to help children throughout Indonesia master key math skills, focusing today on the Square Root of 25/9 with a special emphasis on square roots—in a way that’s fun, lively, and easy to understand. Whether your child is measuring the speed of a roller coaster at Dunia Fantasi, tracking scores in badminton matches, or managing their allowance for the latest gadgets, mastering algebra builds the confidence they need for everyday problems. Our hands-on lessons make learning simple and enjoyable. Because children in Indonesia learn differently, we tailor our approach to fit each learner’s needs. From Jakarta’s bustling streets to Bali’s scenic beaches, BrightChamps brings math to life, making it relevant and exciting across Indonesia. 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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