Square Root of 25/9
2026-02-28 06:00 Diff
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Last updated on August 5, 2025

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.

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.

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

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.

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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.

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.

Problem 1

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

Okay, lets 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.

Well explained 👍

Problem 2

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

Okay, lets 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.

Well explained 👍

Problem 3

Calculate √(25/9) × 4.

Okay, lets 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.

Well explained 👍

Problem 4

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

Okay, lets 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.

Well explained 👍

Problem 5

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

Okay, lets 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.

Well explained 👍

FAQ on Square Root of 25/9

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

The simplest form of √(25/9) is achieved by taking the square root of both the numerator and the denominator separately: √25/√9 = 5/3.

2.Mention the factors of 25/9.

The factors of 25/9 are the factors of 25 and 9 separately.

Factors of 25 are 1, 5, and 25.

Factors of 9 are 1, 3, and 9.

3.Calculate the square of 25/9.

We get the square of 25/9 by multiplying the fraction by itself, that is (25/9) × (25/9) = 625/81.

4.Is 25/9 a prime fraction?

25/9 is not a prime fraction, as both the numerator and the denominator have factors other than 1 and themselves.

5.25/9 is divisible by?

25/9 is divisible by the factors of 25 and 9 separately.

For instance, 25 is divisible by 1, 5, and 25, while 9 is divisible by 1, 3, and 9.

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.

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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.

Fun Fact

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