Square Root of 25.25
2026-02-28 13:49 Diff
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Last updated on August 5, 2025

If a number is multiplied by itself, 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 and finance. Here, we will discuss the square root of 25.25.

What is the Square Root of 25.25?

The square root is the inverse of the square of the number. 25.25 is not a perfect square. The square root of 25.25 is expressed in both radical and exponential form. In the radical form, it is expressed as √25.25, whereas (25.25)^(1/2) in the exponential form. √25.25 = 5.0249378106, which is an irrational number because it cannot be expressed in the form of p/q, where p and q are integers and q ≠ 0.

Finding the Square Root of 25.25

The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, the long-division method and approximation method are used. Let us now learn the following methods:

  • Long division method
  • Approximation method

Square Root of 25.25 by Long Division Method

The long division method is particularly used for non-perfect square numbers. Let us now learn how to find the square root using the long division method, step by step.

Step 1: Start by grouping the digits from right to left in pairs. For 25.25, consider 25 and 25 as separate groups.

Step 2: Find a number whose square is less than or equal to 25. The number is 5, since 5 × 5 = 25. The quotient is 5, and the remainder is 0.

Step 3: Bring down the next pair, which is 25, and place it next to the remainder, making it 025. Add the previous divisor, 5, to itself to get 10.

Step 4: Find a number (n) such that 10n × n ≤ 25. The number is 2, as 102 × 2 = 204, which is less than 250.

Step 5: Subtract 204 from 250, leaving a remainder of 46.

Step 6: Bring down another pair of zeros to make the number 4600.

Step 7: Continue the process until you reach the desired precision.

The quotient, up to two decimal places, is 5.02.

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Square Root of 25.25 by Approximation Method

The approximation method is another way to find square roots. It is an easy method to find the square root of a given number. Now let us learn how to find the square root of 25.25 using the approximation method.

Step 1: Identify the closest perfect squares to 25.25. The closest perfect squares are 25 (5²) and 36 (6²).

Step 2: Apply the formula:

(Given number - smaller perfect square) ÷ (larger perfect square - smaller perfect square).

Step 3: Using the formula, (25.25 - 25) ÷ (36 - 25) = 0.25 ÷ 11 = 0.0227.

Step 4: Add this to the square root of the smaller perfect square: 5 + 0.0227 = 5.0227.

This approximation gives the square root of 25.25 as approximately 5.024.

Common Mistakes and How to Avoid Them in the Square Root of 25.25

Students make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division methods. Let us look at a few common mistakes in detail.

Problem 1

Can you help Max find the area of a square box if its side length is given as √25.25?

Okay, lets begin

The area of the square is 25.25 square units.

Explanation

The area of a square is given by side².

The side length is √25.25, so the area is (√25.25)² = 25.25 square units.

Well explained 👍

Problem 2

A square-shaped building measuring 25.25 square feet is built; if each side is √25.25, what will be the square feet of half of the building?

Okay, lets begin

12.625 square feet

Explanation

Divide the given area by 2 as the building is square-shaped.

Dividing 25.25 by 2 gives 12.625 square feet.

Well explained 👍

Problem 3

Calculate √25.25 × 5.

Okay, lets begin

25.124689053

Explanation

First, find the square root of 25.25, which is approximately 5.0249378106.

Then multiply by 5: 5.0249378106 × 5 = 25.124689053.

Well explained 👍

Problem 4

What will be the square root of (20 + 5.25)?

Okay, lets begin

The square root is 5.0249378106

Explanation

To find the square root, sum (20 + 5.25) = 25.25, and then find √25.25 ≈ 5.0249378106.

Well explained 👍

Problem 5

Find the perimeter of a rectangle if its length ‘l’ is √25.25 units and the width ‘w’ is 8 units.

Okay, lets begin

The perimeter of the rectangle is 26.0498756212 units.

Explanation

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

Perimeter = 2 × (√25.25 + 8) = 2 × (5.0249378106 + 8) = 2 × 13.0249378106 = 26.0498756212 units.

Well explained 👍

FAQ on Square Root of 25.25

1.What is √25.25 in its simplest form?

√25.25 is already in its simplest form as it cannot be simplified further to an integer or common fraction. It is approximately 5.0249378106.

2.Mention the factors of 25.25.

Factors of 25.25 as a decimal are not typically listed, but 25.25 is derived from 101/4, so its factors relate to 101 and 4, which are 1, 2, 4, 25.25, 50.5, and 101.

3.Calculate the square of 25.25.

We get the square of 25.25 by multiplying the number by itself: 25.25 × 25.25 = 637.5625.

4.Is 25.25 a prime number?

25.25 is not a prime number as it is not an integer and has decimal points.

5.25.25 is divisible by?

25.25 is divisible by 1, 5.05, and 25.25.

Important Glossaries for the Square Root of 25.25

  • Square root: The square root of a number is a value that, when multiplied by itself, gives the original number. Example: √25.25 ≈ 5.0249.
     
  • Irrational number: An irrational number cannot be expressed as a simple fraction. It has a non-repeating, non-terminating decimal expansion.
     
  • Principal square root: The principal square root is the positive square root of a number. For example, the principal square root of 25.25 is 5.0249378106.
     
  • Decimal: A decimal is a fraction written in a special form. For example, 0.5 is a decimal and is equal to 1/2.
     
  • Approximation: An approximation is a value or quantity that is nearly but not exactly correct. It is used to estimate values when precise figures are not necessary.

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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.