Square Root of 6/5
2026-02-28 12:06 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-6-by-5

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Last updated on December 15, 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 like vehicle design, finance, etc. Here, we will discuss the square root of 6/5.

What is the Square Root of 6/5?

The square root is the inverse of the square of a number. 6/5 is not a perfect square.

The square root of 6/5 is expressed in both radical and exponential forms.

In the radical form, it is expressed as √(6/5), whereas (6/5)(1/2) in the exponential form.

√(6/5) = 1.09545, 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 6/5

The prime factorization method is useful for perfect square numbers.

However, for non-perfect square numbers, methods like long-division and approximation are used.

Let us now learn the following methods:

  • Prime factorization method
     
  • Long division method
     
  • Approximation method

Square Root of 6/5 by Prime Factorization Method

The product of prime factors is the prime factorization of a number.

Since 6/5 is a fraction, we perform the prime factorization of both the numerator and the denominator.

Step 1: Finding the prime factors of 6 and 5 6 can be broken down into 2 x 3, and 5 is already a prime number.

Step 2: Since 6/5 is not a perfect square, the prime factorization method cannot be directly used to find its square root.

Therefore, using prime factorization for 6/5 is not possible.

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Square Root of 6/5 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: Express 6/5 as a decimal, which is 1.2.

Step 2: Group the whole number and decimal places appropriately. In this case, we start with 1.2.

Step 3: Find n whose square is closest to 1. The closest is 1, as 1 x 1 = 1.

Step 4: Subtract 1 from 1.2 to get 0.2 and bring down two zeros to get 20. The new dividend is 20.

Step 5: Double the divisor, which is 2.

Step 6: Find a number to place next to 2 to form a divisor that multiplied by the same number gives a product less than or equal to 20.

Step 7: Continue the division to obtain the square root to the desired decimal places.

The square root of 6/5 or 1.2 is approximately 1.095.

Square Root of 6/5 by Approximation Method

The approximation method is another way to find the square roots, especially for fractions.

Let us learn how to find the square root of 6/5 using this method.

Step 1: Convert the fraction to its decimal form, which is 1.2.

Step 2: Identify the closest perfect squares. Since 1.2 is between 1 (1²) and 1.44 (1.2²), it falls between 1 and 1.2.

Step 3: Use interpolation or approximation to find the square root. If 1.2 - 1 = 0.2 and 1.44 - 1 = 0.44, then the square root approximately equals 1 + (0.2/0.44) = 1.095.

Therefore, the square root of 6/5 is approximately 1.095.

Common Mistakes and How to Avoid Them in the Square Root of 6/5

Students make mistakes while finding the square root, such as forgetting about the negative square root or skipping long division steps.

Here are a few common mistakes students make.

Problem 1

Can you help Max find the area of a square box if its side length is given as √(6/5)?

Okay, lets begin

The area of the square is approximately 1.2 square units.

Explanation

The area of the square = side².

The side length is √(6/5).

Area of the square = (√(6/5))²

= 6/5

= 1.2

Therefore, the area of the square box is approximately 1.2 square units.

Well explained 👍

Problem 2

A square-shaped building measuring 6/5 square meters is built; if each of the sides is √(6/5), what will be the square meters of half of the building?

Okay, lets begin

0.6 square meters

Explanation

Since the building is square-shaped, we can divide the given area by 2.

Dividing 6/5 by 2 = 0.6 So half of the building measures 0.6 square meters.

Well explained 👍

Problem 3

Calculate √(6/5) × 5.

Okay, lets begin

5.475

Explanation

First, find the square root of 6/5, which is approximately 1.095.

Then, multiply 1.095 by 5. So, 1.095 × 5 = 5.475

Well explained 👍

Problem 4

What will be the square root of (3 + 3/5)?

Okay, lets begin

The square root is approximately 1.264

Explanation

To find the square root, first find the sum of 3 + 3/5. 3 + 3/5 = 3.6, and then calculate √3.6 ≈ 1.897

Therefore, the square root of (3 + 3/5) is approximately ±1.897

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √(6/5) units and the width ‘w’ is 3 units.

Okay, lets begin

We find the perimeter of the rectangle as approximately 8.19 units.

Explanation

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

Perimeter = 2 × (√(6/5) + 3)

= 2 × (1.095 + 3)

= 2 × 4.095

= 8.19 units.

Well explained 👍

FAQ on Square Root of 6/5

1.What is √(6/5) in its simplest form?

The simplest form of √(6/5) is √6/√5, which can be expressed as a decimal approximately equal to 1.095.

2.What are the factors of 6 and 5?

Factors of 6 are 1, 2, 3, and 6.

Factors of 5 are 1 and 5.

3.Calculate the square of 6/5.

The square of 6/5 is (6/5) × (6/5) = 36/25 = 1.44.

4.Is 6/5 a prime number?

6/5 is not a prime number, as it is not an integer.

5.Is 6/5 a rational number?

Important Glossaries for the Square Root of 6/5

  • Square root: A square root is the inverse of squaring a number. Example: 4² = 16, and the inverse of the square is the square root, which is √16 = 4.
  • Irrational number: An irrational number cannot be written in the form of p/q, where q is not equal to zero, and p and q are integers.
  • Rational number: A rational number can be expressed as a ratio of two integers.
  • Fraction: A fraction represents a part of a whole or any number of equal parts, expressed as a ratio of two numbers.
  • Decimal: A decimal is a number that consists of a whole number and a fractional part separated by a decimal point, e.g., 7.86, 8.65, 9.42.

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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.