Square Root of 2.5
2026-02-28 13:17 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 like vehicle design, finance, etc. Here, we will discuss the square root of 2.5.

What is the Square Root of 2.5?

The square root is the inverse of the square of the number. 2.5 is not a perfect square. The square root of 2.5 is expressed in both radical and exponential form. In radical form, it is expressed as √2.5, whereas (2.5)^(1/2) in exponential form. √2.5 ≈ 1.58114, 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 2.5

The prime factorization method is typically used for perfect square numbers. However, for non-perfect square numbers like 2.5, the long-division method and approximation method are used. Let us now learn the following methods:

  • Long division method
  • Approximation method

Square Root of 2.5 by Long Division Method

The long division method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the square root using the long division method, step by step.

Step 1: To begin with, we need to express the number as 2.50 to facilitate division.

Step 2: Find the closest perfect square less than or equal to 2.5, which is 1. Now, 1 × 1 = 1. Subtract 1 from 2.5, giving 1.5.

Step 3: Double the result from step 2, which is 1, to get 2.

Step 4: Bring down two zeros to make it 150. Find a digit n such that 2n × n is less than or equal to 150. The digit n is 5, as 25 × 5 = 125.

Step 5: Subtract 125 from 150, leaving a remainder of 25.

Step 6: Bring down another pair of zeros to get 2500. Repeat the process to get a more accurate result.

Step 7: The square root of 2.5 is approximately 1.58114.

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Square Root of 2.5 by Approximation Method

The approximation method is another method for finding 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 2.5 using the approximation method.

Step 1: Identify the closest perfect squares around 2.5, which are 1 (1^2) and 4 (2^2). √2.5 falls between 1 and 2.

Step 2: Use interpolation to approximate: 2.5 is closer to 4 than to 1, so we estimate a value closer to 1.6.

Step 3: Calculate and refine to find the approximate value: The square root of 2.5 ≈ 1.58.

Common Mistakes and How to Avoid Them in the Square Root of 2.5

Students can make mistakes while finding square roots, such as forgetting about the negative square root, skipping steps in the long division method, etc. Now let us look at a few of those mistakes in detail.

Problem 1

Can you help Max find the area of a square box if its side length is given as √2.5?

Okay, lets begin

The area of the square is approximately 6.25 square units.

Explanation

The area of the square = side^2.

The side length is given as √2.5.

Area of the square = (√2.5) × (√2.5) ≈ 1.58114 × 1.58114 ≈ 2.5.

Therefore, the area of the square box is approximately 2.5 square units.

Well explained 👍

Problem 2

A square-shaped building measuring 2.5 square feet is built; if each of the sides is √2.5, what will be the square feet of half of the building?

Okay, lets begin

1.25 square feet

Explanation

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

Dividing 2.5 by 2, we get 1.25.

So half of the building measures 1.25 square feet.

Well explained 👍

Problem 3

Calculate √2.5 × 5.

Okay, lets begin

Approximately 7.9057

Explanation

The first step is to find the square root of 2.5, which is approximately 1.58114.

The second step is to multiply 1.58114 by 5.

So, 1.58114 × 5 ≈ 7.9057.

Well explained 👍

Problem 4

What will be the square root of (2 + 0.5)?

Okay, lets begin

The square root is approximately 1.58114.

Explanation

To find the square root, we need to find the sum of (2 + 0.5). 2 + 0.5 = 2.5, and then √2.5 ≈ 1.58114.

Therefore, the square root of (2 + 0.5) is approximately ±1.58114.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length 'l' is √2.5 units and the width 'w' is 3 units.

Okay, lets begin

The perimeter of the rectangle is approximately 9.16228 units.

Explanation

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

Perimeter = 2 × (√2.5 + 3) ≈ 2 × (1.58114 + 3) ≈ 2 × 4.58114 ≈ 9.16228 units.

Well explained 👍

FAQ on Square Root of 2.5

1.What is √2.5 in its simplest form?

The simplest form of √2.5 is not expressible as a simple radical since 2.5 is not a perfect square.

2.Is 2.5 a perfect square?

No, 2.5 is not a perfect square because it cannot be expressed as the square of an integer.

3.Calculate the square of 2.5.

The square of 2.5 is 6.25, as 2.5 × 2.5 = 6.25.

4.Is 2.5 a prime number?

5.What are the factors of 2.5?

The factors of 2.5 are 1, 2.5, and 0.5.

Important Glossaries for the Square Root of 2.5

  • Square root: A square root is a value that, when multiplied by itself, gives the original number. Example: √4 = 2, since 2 × 2 = 4.
  • Irrational number: An irrational number cannot be written as a simple fraction, and its decimal form is non-repeating and non-terminating.
  • Approximation method: A method to estimate the square root by identifying the closest perfect squares and using interpolation.
  • Long division method: A step-by-step way to find the square root of a number by dividing, multiplying, and subtracting.
  • Decimal: A number that includes a whole number and a fractional part separated by a decimal point, such as 1.58114.

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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.