Square Root of 4/5
2026-02-28 06:02 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-4/5

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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 4/5.

What is the Square Root of 4/5?

The square root is the inverse of squaring a number. 4/5 is not a perfect square. The square root of 4/5 can be expressed in both radical and exponential form. In radical form, it is expressed as √(4/5), whereas in exponential form, it is expressed as (4/5)^(1/2). √(4/5) = √4/√5 = 2/√5. This is an irrational number because it cannot be expressed as a simple fraction p/q, where p and q are integers and q ≠ 0.

Finding the Square Root of 4/5

The prime factorization method is typically used for perfect square numbers. For non-perfect square numbers like 4/5, we use simplification and rationalization. Let us learn the following methods:

Simplification and rationalization Decimal approximation

Square Root of 4/5 by Simplification and Rationalization

To find the square root of a fraction, we take the square root of the numerator and the denominator separately.

Step 1: Find the square roots of the numerator and the denominator separately. √4 = 2 and √5 is left as is because it is an irrational number.

Step 2: Express the square root of the fraction. √(4/5) = √4/√5 = 2/√5.

Step 3: Rationalize the denominator. Multiply both the numerator and the denominator by √5 to remove the radical from the denominator: (2/√5) × (√5/√5) = 2√5/5.

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Square Root of 4/5 by Decimal Approximation

Decimal approximation is another method to find the square root of a given number.

Step 1: Find the decimal form of 4/5, which is 0.8.

Step 2: Use a calculator to approximate √0.8. √0.8 ≈ 0.8944.

Common Mistakes and How to Avoid Them in the Square Root of 4/5

Students often make mistakes when calculating square roots, such as forgetting about the negative square root, skipping steps in rationalization, or misapplying decimal approximations. Here, we will explore some common mistakes in detail.

Problem 1

A rectangle has an area of 4/5 square units. What is the length of a side if it is a square?

Okay, lets begin

The side length is approximately 0.8944 units.

Explanation

Since the area of the square is 4/5, which is 0.8, the side length is the square root of the area. √0.8 ≈ 0.8944.

Therefore, the side length is approximately 0.8944 units.

Well explained 👍

Problem 2

If you multiply the square root of 4/5 by 5, what is the result?

Okay, lets begin

The result is approximately 4.472.

Explanation

First, find the square root of 4/5, which is approximately 0.8944.

Multiply this by 5: 0.8944 × 5 = 4.472.

Well explained 👍

Problem 3

What is the square root of (4/5)²?

Okay, lets begin

The square root is 4/5.

Explanation

The square root of a square returns the original number: √((4/5)²) = 4/5.

Well explained 👍

FAQ on Square Root of 4/5

1.What is √(4/5) in its simplest form?

The simplest form of √(4/5) is 2/√5, which can be rationalized to 2√5/5.

2.Is 4/5 a rational number?

Yes, 4/5 is a rational number because it can be expressed as a fraction of two integers, 4 and 5, where the denominator is not zero.

3.What is the decimal value of √(4/5)?

The decimal approximation of √(4/5) is approximately 0.8944.

4.Can √(4/5) be expressed as a whole number?

No, √(4/5) cannot be expressed as a whole number or a simple fraction. It is an irrational number.

5.How do you rationalize the denominator of 2/√5?

To rationalize the denominator of 2/√5, multiply the numerator and the denominator by √5: (2/√5) × (√5/√5) = 2√5/5.

Important Glossaries for the Square Root of 4/5

  • Square root: The square root of a number is a value that, when multiplied by itself, gives the original number. Example: √9 = 3 because 3 × 3 = 9.
     
  • Irrational number: An irrational number cannot be expressed as a simple fraction. It is non-repeating and non-terminating in decimal form.
     
  • Rationalization: The process of eliminating a radical from the denominator of a fraction by multiplying the numerator and the denominator by a suitable radical.
     
  • Decimal approximation: The process of finding a decimal number close to the value of an irrational number.
     
  • Fraction: A numerical quantity that is not a whole number, represented by two integers, a numerator and a denominator.

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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.