Square Root of 25/4
2026-02-28 06:01 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 fields such as vehicle design, finance, etc. Here, we will discuss the square root of 25/4.

What is the Square Root of 25/4?

The square root is the inverse of the square of the number. 25/4 is a perfect square. The square root of 25/4 can be expressed in both radical and exponential form. In the radical form, it is expressed as √(25/4), whereas (25/4)^(1/2) in the exponential form. √(25/4) = 5/2 = 2.5, 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 25/4

The prime factorization method and direct calculation can be used for perfect square numbers. Since 25/4 is a perfect square, we can directly calculate its square root. Let us now learn the following method:

  • Direct Calculation Method

Square Root of 25/4 by Direct Calculation Method

Since 25/4 is a fraction, we can find its square root by finding the square root of the numerator and the denominator separately.

Step 1: Find the square root of the numerator, which is 25. The square root of 25 is 5.

Step 2: Find the square root of the denominator, which is 4. The square root of 4 is 2.

Step 3: Combine the square roots to form a fraction.

Therefore, the square root of 25/4 is 5/2, which is equal to 2.5.

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Common Mistakes and How to Avoid Them in the Square Root of 25/4

Students do make mistakes while finding the square root, such as forgetting about the negative square root or not simplifying the fraction properly. Let us look at a few of these mistakes in detail.

Common Mistakes and How to Avoid Them in the Square Root of 25/4

Students do make mistakes while finding the square root, such as forgetting about the negative square root or not simplifying fractions properly. Let us look at a few of these mistakes in detail.

Problem 1

Can you help Max find the area of a square box if its side length is given as √(25/4)?

Okay, lets begin

The area of the square is 6.25 square units.

Explanation

The area of the square = side².

The side length is given as √(25/4) = 5/2 = 2.5.

Area of the square = side²

= 2.5 × 2.5

= 6.25.

Therefore, the area of the square box is 6.25 square units.

Well explained 👍

Problem 2

A square-shaped garden measuring 25/4 square meters is built; if each of the sides is √(25/4), what will be the square meters of half of the garden?

Okay, lets begin

3.125 square meters

Explanation

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

Dividing 25/4 by 2 = (25/4) / 2 = 25/8 = 3.125.

So half of the garden measures 3.125 square meters.

Well explained 👍

Problem 3

Calculate √(25/4) × 5.

Okay, lets begin

12.5

Explanation

The first step is to find the square root of 25/4, which is 2.5. The second step is to multiply 2.5 by 5. So, 2.5 × 5 = 12.5.

Well explained 👍

Problem 4

What will be the square root of (25/4 + 0)?

Okay, lets begin

The square root is 2.5

Explanation

To find the square root, we need to determine the sum of (25/4 + 0). 25/4 + 0 = 25/4, and then √(25/4) = 2.5.

Therefore, the square root of (25/4 + 0) is ±2.5.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √(25/4) units and the width ‘w’ is 4 units.

Okay, lets begin

We find the perimeter of the rectangle as 13 units.

Explanation

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

Perimeter = 2 × (2.5 + 4)

= 2 × 6.5

= 13 units.

Well explained 👍

FAQ on Square Root of 25/4

1.What is √(25/4) in its simplest form?

The simplest form of √(25/4) is 5/2, which can also be written as 2.5.

2.Mention the factors of 25/4.

The factors of 25/4 in its simplest form are 5 and 2.

3.Calculate the square of 25/4.

We get the square of 25/4 by multiplying the number by itself, that is (25/4) × (25/4) = 625/16 = 39.0625.

4.Is 25/4 a rational number?

Yes, 25/4 is a rational number because it can be expressed as the quotient of two integers.

5.Is 25/4 a perfect square?

Yes, 25/4 is a perfect square because both 25 and 4 are perfect squares, and their square roots are integers.

Important Glossaries for the Square Root of 25/4

  • Square root: A square root is the inverse of a square. For example, 4² = 16 and the inverse of the square is the square root, that is √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.
     
  • Perfect square: A perfect square is a number that is the square of an integer. For example, 25 and 4 are perfect squares because they are squares of 5 and 2, respectively.
  • Fraction: A fraction represents a part of a whole or, more generally, any number of equal parts. It is expressed as the quotient of two numbers, the numerator over the denominator.
     
  • Principal square root: A number has both positive and negative square roots; however, it is usually the positive square root that is used in real-world applications. This is known as the principal square root.

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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.