Square Root of 9/5
2026-02-28 06:14 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-9/5

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Last updated on August 5, 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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 9/5.

What is the Square Root of 9/5?

The square root is the inverse of the square of the number. 9/5 is not a perfect square. The square root of 9/5 is expressed in both radical and exponential form. In radical form, it is expressed as √(9/5), whereas (9/5)^(1/2) in exponential form. √(9/5) = √9/√5 = 3/√5 = 3√5/5, 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 9/5

The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers such as fractions, where rationalizing the denominator is often used. Let us now learn the following methods:

  • Rationalizing the denominator
  • Decimal approximation

Square Root of 9/5 by Rationalizing the Denominator

Rationalizing the denominator involves converting a fraction with a square root in the denominator into an equivalent fraction with a rational denominator.

Step 1: Identify the square root in the denominator. Here, it is √5.

Step 2: Multiply both the numerator and the denominator by √5 to eliminate the square root from the denominator. (3/√5) × (√5/√5) = (3√5)/5

Step 3: Now, the expression is rationalized, with the square root remaining only in the numerator.

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Square Root of 9/5 by Decimal Approximation

Decimal approximation is another method for finding square roots, and it is useful for estimating the value.

Step 1: Calculate the decimal form of 9/5, which is 1.8.

Step 2: Find the square root of 1.8 using a calculator or estimation, which is approximately 1.3416.

Mistakes to Avoid When Finding the Square Root of 9/5

Students often make mistakes when working with square roots, especially with fractions. Here are some common mistakes and how to avoid them:

Forgetting to Rationalize the Denominator

When dealing with square roots of fractions, it's crucial to rationalize the denominator.For instance, leaving the answer as 3/√5 without rationalizing would be incorrect in some contexts. Always multiply by the conjugate to rationalize.

Common Mistakes and How to Avoid Them in the Square Root of 9/5

Students do make mistakes while finding the square root, like forgetting to rationalize the denominator or ignoring the negative square root. Skipping steps in calculation can also lead to errors. Now let us look at a few of those mistakes that students tend to make in detail.

Problem 1

Can you help Max find the area of a square if its side length is given as √(9/5)?

Okay, lets begin

The area of the square is approximately 1.8 square units.

Explanation

The area of the square = side².

The side length is given as √(9/5).

Area of the square = side²

= (√(9/5))²

= 9/5

= 1.8.

Therefore, the area of the square is 1.8 square units.

Well explained 👍

Problem 2

A square-shaped park measuring 9/5 square units is created. If each of the sides is √(9/5), what will be the total length of the boundary of the park?

Okay, lets begin

Approximately 5.3664 units.

Explanation

The perimeter of a square = 4 × side.

Side length = √(9/5)

≈ 1.3416.

Perimeter = 4 × 1.3416

≈ 5.3664 units.

Well explained 👍

Problem 3

Calculate √(9/5) × 10.

Okay, lets begin

Approximately 13.416.

Explanation

First, find the square root of 9/5, which is approximately 1.3416.

Then, multiply 1.3416 by 10.

So, 1.3416 × 10 ≈ 13.416.

Well explained 👍

Problem 4

What will be the square root of (45/25)?

Okay, lets begin

The square root is 3/5.

Explanation

To find the square root, we need to simplify (45/25) to (9/5).

Then, √(9/5) = 3/√5 = 3√5/5.

Therefore, the square root of (45/25) is 3/5.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √(9/5) units and the width ‘w’ is 5 units.

Okay, lets begin

The perimeter of the rectangle is approximately 12.6832 units.

Explanation

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

Perimeter = 2 × (√(9/5) + 5)

Perimeter = 2 × (1.3416 + 5)

Perimeter ≈ 2 × 6.3416

≈ 12.6832 units.

Well explained 👍

FAQ on Square Root of 9/5

1.What is √(9/5) in its simplest form?

The simplest form of √(9/5) is (3√5)/5 after rationalizing the denominator.

2.Is 9/5 a perfect square?

No, 9/5 is not a perfect square because its square root is not a rational number.

3.What is the decimal approximation of √(9/5)?

The decimal approximation of √(9/5) is approximately 1.3416.

4.Does √(9/5) have a negative value?

Yes, like any square root, √(9/5) has both positive and negative values: ±1.3416.

5.Can you express √(9/5) as a fraction?

√(9/5) is an irrational number, so it cannot be expressed as a simple fraction, but it can be approximated as (3√5)/5.

Important Glossaries for the Square Root of 9/5

  • Square root: A square root is the inverse of a square. For example, 4² = 16, and the inverse of the square is the square root, which is √16 = 4.
     
  • Irrational number: An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.
     
  • Rationalizing the denominator: The process of eliminating a square root from the denominator of a fraction by multiplying both the numerator and denominator by an appropriate value.
     
  • Decimal approximation: An estimated value of a number that cannot be precisely expressed as a simple fraction but is represented in decimal form.
     
  • Fraction: A mathematical expression representing the division of one integer by another. For example, 9/5 is a fraction.

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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.