Square Root of 1/25
2026-02-28 06:16 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1/25

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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 fields such as vehicle design, finance, etc. Here, we will discuss the square root of 1/25.

What is the Square Root of 1/25?

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

The prime factorization method is used for perfect square numbers. Since 1/25 is a perfect square, we can use the prime factorization method. Alternatively, the long division method and approximation method are also suitable for verification. Let us now learn the following methods:

  • Prime factorization method
     
  • Long division method

  • Approximation method

Square Root of 1/25 by Prime Factorization Method

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

Step 1: Finding the prime factors of 25 Breaking it down, we get 5 x 5: 5²

Step 2: Since 1 is already a perfect square (1²), the prime factorization of 1/25 is 1/(5²).

Step 3: Taking the square root of 1/25 gives us 1/5.

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Square Root of 1/25 by Long Division Method

The long division method is another method that can be used for perfect square numbers. Here is how you find the square root of 1/25 using long division:

Step 1: Express 1/25 as a decimal, which is 0.04.

Step 2: Group the digits of 0.04 as 00 and 04.

Step 3: Find a number whose square is closest to 0.04. Here, 0.2 x 0.2 = 0.04.

Step 4: Therefore, the square root of 0.04 is 0.2, which equals 1/5.

Square Root of 1/25 by Approximation Method

The approximation method is another method for finding square roots. It's an easy method to understand the square root of a given number. Let's learn how to find the square root of 1/25 using the approximation method:

Step 1: Approximate 1/25 to the nearest perfect square. The closest perfect square to 0.04 is 0.04 itself.

Step 2: The square root of 0.04 is 0.2.

Step 3: Therefore, the square root of 1/25 is 1/5.

Common Mistakes and How to Avoid Them in the Square Root of 1/25

Students can make mistakes while finding the square root, such as forgetting about the negative square root, skipping steps in methods, etc. 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 area of a square box if its side length is given as √(1/25)?

Okay, lets begin

The area of the square is 1/25 square units.

Explanation

The area of the square = side².

The side length is given as √(1/25), which is 1/5.

Area of the square = (1/5)² = 1/25.

Therefore, the area of the square box is 1/25 square units.

Well explained 👍

Problem 2

A square-shaped building measuring 1/25 square meters is built; if each of the sides is √(1/25), what will be the square meters of half of the building?

Okay, lets begin

1/50 square meters

Explanation

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

Dividing 1/25 by 2 = 1/50.

So, half of the building measures 1/50 square meters.

Well explained 👍

Problem 3

Calculate √(1/25) x 5.

Okay, lets begin

1

Explanation

The first step is to find the square root of 1/25, which is 1/5.

The second step is to multiply 1/5 by 5.

So, (1/5) x 5 = 1.

Well explained 👍

Problem 4

What will be the square root of (1/25 + 24/25)?

Okay, lets begin

The square root is 1.

Explanation

To find the square root, we need to find the sum of (1/25 + 24/25). 1/25 + 24/25 = 25/25 = 1, and then √1 = ±1. Therefore, the square root of (1/25 + 24/25) is ±1.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √(1/25) units and the width ‘w’ is 10 units.

Okay, lets begin

The perimeter of the rectangle is 20.4 units.

Explanation

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

Perimeter = 2 × (1/5 + 10) = 2 × (0.2 + 10) = 2 × 10.2 = 20.4 units.

Well explained 👍

FAQ on Square Root of 1/25

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

The prime factorization of 25 is 5 x 5, so the simplest form of √(1/25) is 1/5.

2.Mention the factors of 25.

Factors of 25 are 1, 5, and 25.

3.Calculate the square of 1/5.

We get the square of 1/5 by multiplying the number by itself, that is (1/5) x (1/5) = 1/25.

4.Is 1/25 a perfect square?

Yes, 1/25 is a perfect square because its square root is a rational number, 1/5.

5.1/25 is divisible by?

1/25 is divisible by 1/25, 1/5, and 1.

Important Glossaries for the Square Root of 1/25

  • Square root: A square root is the inverse of a square. Example: 5² = 25, and the inverse of the square is the square root, that is, √25 = 5.
  • Perfect square: A perfect square is a number that is the square of an integer. Example: 25 is a perfect square because it is 5².
  • Rational number: A rational number is a number that can be expressed in the form of p/q, where q ≠ 0 and p and q are integers.
  • Decimal: A decimal is a number that has a whole number and a fraction in a single number, such as 0.2, 1.5, and 3.75.
  • Principal square root: The principal square root is the positive square root of a number. For example, the principal square root of 25 is 5.

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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.