Square Root of 1.25
2026-02-28 08:37 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1.25

389 Learners

Last updated on August 5, 2025

If a number is multiplied by itself, the result is a square. The inverse of the square is the square root. The square root is used in fields like 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 squaring a number. 1.25 is not a perfect square. The square root of 1.25 can be expressed in radical form as √1.25, and in exponential form as (1.25)^(1/2). The value of √1.25 is approximately 1.1180339887, which is an irrational number since it cannot be expressed as a simple fraction.

Finding the Square Root of 1.25

For calculating the square root of non-perfect squares like 1.25, methods such as the long division method and approximation method are used. Let's explore these methods:

  • Long division method
     
  • Approximation method

Square Root of 1.25 by Long Division Method

The long division method is effective for finding the square root of non-perfect squares. Let's find the square root of 1.25 using this method step by step:

Step 1: Pair the digits from right to left; here, 1 and 25 are paired as 1.25.

Step 2: Find the largest number whose square is less than or equal to 1. Only 1 fits this condition. Now, the quotient is 1, and the remainder is 0.

Step 3: Bring down 25, making the new dividend 125. Double the quotient, which gives us 2, our new divisor.

Step 4: Find a number (n) such that 2n × n is less than or equal to 125. Here, n is 5 because 25 × 5 = 125.

Step 5: Subtract 125 from 125, resulting in 0.

Step 6: Since the remainder is zero, the square root of 1.25 is 1.118 approximately.

Explore Our Programs

Square Root of 1.25 by Approximation Method

The approximation method is a straightforward way to find the square root of a number. Let's find the square root of 1.25 using this method:

Step 1: Identify perfect squares between which 1.25 lies. The closest perfect square below 1.25 is 1 (√1 = 1), and above is 1.44 (√1.44 = 1.2).

Step 2: Use interpolation to approximate the square root: (1.25 - 1) / (1.44 - 1) = 0.25 / 0.44 ≈ 0.568

Step 3: Add this decimal to the square root of the smaller perfect square: 1 + 0.568 ≈ 1.118

Thus, the square root of 1.25 is approximately 1.118.

Common Mistakes and How to Avoid Them in the Square Root of 1.25

Students often make mistakes while finding square roots, such as overlooking the negative square root or skipping steps in the long division method. Let’s review some 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 √1.25?

Okay, lets begin

The area of the square is approximately 1.25 square units.

Explanation

The area of a square is given by side².

The side length is √1.25.

Area = (√1.25)² = 1.25.

Therefore, the area of the square box is approximately 1.25 square units.

Well explained 👍

Problem 2

A square-shaped building measures 1.25 square meters in area. What is the side length of the building?

Okay, lets begin

The side length is approximately 1.118 meters.

Explanation

The side length of a square with area A is √A.

Side length = √1.25 ≈ 1.118 meters.

Well explained 👍

Problem 3

Calculate √1.25 × 5.

Okay, lets begin

Approximately 5.59

Explanation

First, find the square root of 1.25, which is approximately 1.118.

Then multiply by 5: 1.118 × 5 ≈ 5.59.

Well explained 👍

Problem 4

What will be the square root of (0.5 + 0.75)?

Okay, lets begin

The square root is approximately 1.118.

Explanation

First, find the sum: 0.5 + 0.75 = 1.25.

The square root of 1.25 is approximately 1.118.

Well explained 👍

Problem 5

Find the perimeter of a rectangle if its length ‘l’ is √1.25 units and the width ‘w’ is 2 units.

Okay, lets begin

The perimeter of the rectangle is approximately 6.236 units.

Explanation

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

Perimeter = 2 × (√1.25 + 2) ≈ 2 × (1.118 + 2) = 6.236 units.

Well explained 👍

FAQ on Square Root of 1.25

1.What is √1.25 in its simplest form?

The simplest form of √1.25 is approximately 1.118, as it cannot be simplified further in radical form.

2.Mention the factors of 1.25.

Factors of 1.25 include 1, 1.25, 0.25, and 5.

3.Calculate the square of 1.25.

To find the square of 1.25, multiply it by itself: 1.25 × 1.25 = 1.5625.

4.Is 1.25 a prime number?

5.1.25 is divisible by?

1.25 is divisible by 1 and 0.25.

Important Glossaries for the Square Root of 1.25

  • Square root: A square root is the inverse of squaring a number. For example, 3² = 9, and the inverse of this is √9 = 3.
  • Irrational number: An irrational number cannot be expressed as a fraction of two integers. For example, √2 is irrational.
  • Radical form: Radical form refers to the expression of a number using a root symbol, such as √1.25.
  • Decimal approximation: Decimal approximation is expressing a number with a finite number of decimal places, often used for irrational numbers.
  • Perfect square: A perfect square is a number that is the square of an integer. For example, 4 is a perfect square because it is 2².

What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math

▶

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.