Square Root of 4/3
2026-02-28 06:20 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-4/3

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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 various fields such as engineering, physics, and statistics. Here, we will discuss the square root of 4/3.

What is the Square Root of 4/3?

The square root is the inverse of the square of the number. 4/3 is not a perfect square. The square root of 4/3 is expressed in both radical and exponential form. In the radical form, it is expressed as √(4/3), whereas (4/3)^(1/2) in the exponential form. √(4/3) = √4/√3 = 2/√3, which can also be expressed as (2√3)/3 when rationalized. This 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 4/3

The prime factorization method is used for perfect square numbers. However, for non-perfect squares like 4/3, the simplifying radical and rationalization method are used. Let us now learn these methods:

  • Simplifying radical form
  • Rationalization

Square Root of 4/3 by Simplifying Radical Form

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

Step 1: Identify the square root of the numerator, √4, which is 2.

Step 2: Identify the square root of the denominator, √3, which remains √3 because 3 is not a perfect square.

Step 3: Combine these results as a fraction, resulting in √(4/3) = 2/√3.

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Square Root of 4/3 by Rationalization

Rationalization involves eliminating the radical from the denominator.

Step 1: Start with the fraction 2/√3.

Step 2: Multiply both the numerator and the denominator by √3 to eliminate the radical from the denominator.

Step 3: This results in (2√3)/(√3 × √3) = (2√3)/3.

Common Mistakes and How to Avoid Them in the Square Root of 4/3

Students often make mistakes when dealing with square roots, such as forgetting to rationalize or misapplying the properties of radicals. Let's explore some of these errors in detail.

Problem 1

Can you help Max find the length of the diagonal of a square if its side length is √(4/3)?

Okay, lets begin

The diagonal of the square is approximately 2.309401 units.

Explanation

The diagonal of a square can be found using the formula √2 × side length.

The side length is √(4/3).

Diagonal = √2 × √(4/3) = √(8/3) = 2√(2/3) ≈ 2.309401.

Well explained 👍

Problem 2

A rectangular field has an area of 4/3 square meters, with the length being twice the square root of 4/3. What is the width?

Okay, lets begin

The width is approximately 0.57735 meters.

Explanation

Let the width be 'w'.

Area = length × width = (2 × √(4/3)) × w = 4/3.

w = (4/3) / (2 × √(4/3)) = 1/(2√(4/3)) = 1/((4√3)/3) = √3/4. Width ≈ 0.57735 meters.

Well explained 👍

Problem 3

Calculate √(4/3) × 6.

Okay, lets begin

Approximately 4.6188.

Explanation

First, find the square root of 4/3 which is (2√3)/3.

√(4/3) × 6 = (2√3)/3 × 6 = 4√3 ≈ 4.6188.

Well explained 👍

Problem 4

What will be the square root of (4/3 + 8/3)?

Okay, lets begin

The square root is approximately 1.8257.

Explanation

First, find the sum of (4/3 + 8/3) = 12/3 = 4.

Then the square root of 4 is ±2.

Therefore, the principal square root is 2.

Well explained 👍

Problem 5

Find the perimeter of a rectangle if its length ‘l’ is √(4/3) units and the width ‘w’ is 2 units.

Okay, lets begin

The perimeter of the rectangle is approximately 7.3333 units.

Explanation

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

Perimeter = 2 × (√(4/3) + 2) = 2 × ((2√3)/3 + 2) ≈ 7.3333 units.

Well explained 👍

FAQ on Square Root of 4/3

1.What is √(4/3) in its simplest form?

2.What is the decimal approximation of √(4/3)?

The decimal approximation of √(4/3) is approximately 1.1547.

3.Is 4/3 a perfect square?

No, 4/3 is not a perfect square, as it does not result in an integer when its square root is taken.

4.Is √(4/3) rational or irrational?

√(4/3) is an irrational number, as it cannot be expressed as a ratio of two integers.

5.What is the square of √(4/3)?

The square of √(4/3) is 4/3, as squaring a square root returns the original number.

Important Glossaries for the Square Root of 4/3

  • Square root: A square root is the inverse of a square. Example: 4 = 2², and the inverse of the square is the square root, √4 = 2.
  • Irrational number: An irrational number cannot be expressed as a ratio of two integers. For example, √3 is irrational.
  • Rationalization: The process of eliminating a radical from the denominator of a fraction.
  • Radical: An expression that uses the root symbol, such as √3, which denotes the square root of 3.
  • Fraction: A numerical quantity that is not a whole number, represented by two numbers separated by a slash, like 4/3.

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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.