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236 LearnersLast updated on December 15, 2025
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.
Mistake 1
Forgetting about the negative square root
It is important to remember that a number has both positive and negative square roots.
However, we generally take only the positive square root for practical applications.
For example: √(6/5) = 1.095, but there is also -1.095, which should not be forgotten.
Mistake 2
Not adding square root symbols in proper places
Not using the square root symbol properly is a common mistake.
To resolve this, it's essential to simplify the numbers inside the square root first.
For example: √(a + b) ≠ √a + √b.
Mistake 3
Not finding the correct value of a non-perfect square
Students often make mistakes in approximating the value of non-perfect squares.
Proper techniques should be taught to avoid errors.
For example: √50 ≠ 7; the correct answer is √50 ≈ 7.071.
Mistake 4
Confusing the square root symbol with the cube root
Students need to understand the difference between cube roots and square roots.
For instance, √8 and ∛8 are different.
Mistake 5
Making mistakes in long division
The long division method involves several steps, and missing a step can result in errors.
Students should practice carefully to avoid such mistakes.
Square Root of 6/5 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √(6/5)?
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.
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?
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.
Problem 3
Calculate √(6/5) × 5.
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
Problem 4
What will be the square root of (3 + 3/5)?
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
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √(6/5) units and the width ‘w’ is 3 units.
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.
FAQ on Square Root of 6/5
1.What is √(6/5) in its simplest form?
2.What are the factors of 6 and 5?
3.Calculate the square of 6/5.
4.Is 6/5 a prime number?
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.
Vikrant Sharma
About the Author
Vikrant is a passionate Mathematics teacher with over 5 years of teaching experience in both conventional and Vedic Maths. His student-focused approach combines clear concepts with motivation and encouragement, helping students build confidence and develo
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
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