Square Root of 9/25
2026-02-28 12:05 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-9-by-25

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Last updated on December 15, 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 fields such as vehicle design, finance, etc. Here, we will discuss the square root of 9/25.

What is the Square Root of 9/25?

The square root is the inverse of the square of a number. 9/25 is a perfect square.

The square root of 9/25 can be expressed in both radical and exponential form.

In radical form, it is expressed as √(9/25), whereas in exponential form it is (9/25)(1/2).

√(9/25) = √9/√25 = 3/5, 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 9/25

The prime factorization method can be used for finding the square root of perfect square numbers, like 9/25.

However, other methods such as the long division method and approximation method are not needed in this case.

Let's learn how to find the square root of 9/25 using the prime factorization method:

  • Prime factorization method
  • Rationalization method
  • Approximation method

Square Root of 9/25 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Let us look at how 9/25 is broken down into its prime factors:

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

Step 2: Now we have found out the prime factors of both 9 and 25. Since both 9 and 25 are perfect squares, we can take the square root of each: √(9/25) = √9/√25 = 3/5

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Square Root of 9/25 by Rationalization Method

The rationalization method is particularly used for perfect square fractions.

In this method, we take the square root of the numerator and the square root of the denominator separately.

Let us now learn how to find the square root using this method, step by step:

Step 1: Take the square root of the numerator: √9 = 3

Step 2: Take the square root of the denominator: √25 = 5

Step 3: The square root of the fraction is the quotient of these square roots: √(9/25) = 3/5

Square Root of 9/25 by Approximation Method

The approximation method is not necessary for finding the square root of 9/25, as it is a perfect square fraction.

However, if needed, we would look at the closest perfect square fractions and use them to approximate.

In this case, we directly find the square root as 3/5.

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

Students often make mistakes while finding the square root, such as forgetting about the negative square root or misapplying the square root to the numerator or denominator.

Here are a few common mistakes and how to avoid them.

Problem 1

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

Okay, lets begin

The area of the square is 9/25 square units.

Explanation

The area of the square = side2.

The side length is given as √(9/25).

Area of the square = side2 = (3/5) x (3/5) = 9/25.

Therefore, the area of the square box is 9/25 square units.

Well explained 👍

Problem 2

A square-shaped building measuring 9/25 square meters is built; if each of the sides is √(9/25), what will be the square meters of half of the building?

Okay, lets begin

4.5/25 square meters

Explanation

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

Dividing 9/25 by 2 = we get 4.5/25.

So half of the building measures 4.5/25 square meters.

Well explained 👍

Problem 3

Calculate √(9/25) x 5.

Okay, lets begin

3

Explanation

First, find the square root of 9/25, which is 3/5.

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

So 3/5 x 5 = 3.

Well explained 👍

Problem 4

What will be the square root of (9/25 + 16/25)?

Okay, lets begin

The square root is 1.

Explanation

To find the square root, we need to find the sum of (9/25 + 16/25). 9/25 + 16/25 = 25/25 = 1, and then √1 = 1.

Therefore, the square root of (9/25 + 16/25) is ±1.

Well explained 👍

Problem 5

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

Okay, lets begin

We find the perimeter of the rectangle as 13/5 units.

Explanation

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

Perimeter = 2 × (√(9/25) + 3) = 2 × (3/5 + 15/5) = 2 × 18/5 = 36/5 units.

Well explained 👍

FAQ on Square Root of 9/25

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

The prime factorization of 9 is 3 x 3 and for 25 is 5 x 5.

So, the simplest form of √(9/25) = 3/5.

2.Mention the factors of 9/25.

The factors of 9/25 are: for 9, the factors are 1, 3, 9; for 25, the factors are 1, 5, 25.

3.Calculate the square of 9/25.

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

4.Is 9/25 a rational number?

Yes, 9/25 is a rational number because it can be expressed as a fraction where both the numerator and the denominator are integers.

5.9/25 is divisible by?

The fraction 9/25 in its simplest form is not divisible by any number other than 1 without resulting in a non-integer.

Important Glossaries for the Square Root of 9/25

  • Square root: A square root is the inverse of a square. Example: 42 = 16 and the inverse of the square is the square root which 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. For example, 9 and 25 are perfect squares.
  • Fraction: A fraction consists of a numerator and a denominator and represents a part of a whole.
  • Prime factorization: Breaking down a number into its prime factors. For example, the prime factorization of 9 is 3 x 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.

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