Square Root of 8/3
2026-02-28 10:58 Diff
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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 vehicle design, finance, etc. Here, we will discuss the square root of 8/3.

What is the Square Root of 8/3?

The square root is the inverse of the square of a number. 8/3 is not a perfect square. The square root of 8/3 can be expressed in both radical and exponential form. In radical form, it is expressed as √(8/3), whereas in exponential form, it is (8/3)^(1/2). The square root of 8/3 is approximately 1.63299, 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 8/3

The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, methods such as the long-division method and approximation method are used. Let us now learn the following methods: 

  • Prime factorization method 
  • Long division method 
  • Approximation method

Square Root of 8/3 by Long Division Method

The long division method is particularly used for non-perfect square numbers. Let us now learn how to find the square root of 8/3 using the long division method, step by step:

Step 1: Convert the fraction 8/3 to a decimal, which is approximately 2.6667.

Step 2: Group the digits from left to right.

Step 3: Find a number whose square is less than or equal to 2.66. Begin with 1 since 1 x 1 = 1.

Step 4: Subtract 1 from 2.66, bringing down the next pair of digits.

Step 5: Double the current quotient and find a suitable digit to append to it, which when multiplied by itself, gives a product less than or equal to the current dividend. Repeat these steps until the desired accuracy is achieved.

The square root of 8/3 is approximately 1.63299.

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Square Root of 8/3 by Approximation Method

The approximation method is another way to find square roots. It is an easy method for estimating the square root of a given number. Here's how to find the square root of 8/3 using the approximation method:

Step 1: Approximate the fraction 8/3 as the decimal 2.6667.

Step 2: Identify the closest perfect squares around 2.6667. The perfect squares 1 (1^2) and 4 (2^2) bracket 2.6667.

Step 3: Use interpolation to estimate between these two values. The linear approximation will give you a result close to 1.63299.

Common Mistakes and How to Avoid Them in Finding the Square Root of 8/3

Students often make mistakes while finding square roots, such as forgetting about the negative square root, skipping long division steps, etc. Let us look at a few of these mistakes in detail.

Problem 1

Can you help Max find the area of a square box if its side length is given as √(8/3)?

Okay, lets begin

The area of the square is approximately 2.667 square units.

Explanation

The area of a square = side^2.

If the side length is √(8/3), then the area = (√(8/3))^2 = 8/3 ≈ 2.667 square units.

Well explained 👍

Problem 2

A square-shaped garden covers an area of 8/3 square meters. What is the length of each side of the garden?

Okay, lets begin

The length of each side is approximately 1.633 meters.

Explanation

The side length of a square is the square root of its area.

Thus, the side length is √(8/3) ≈ 1.633 meters.

Well explained 👍

Problem 3

Calculate √(8/3) x 5.

Okay, lets begin

Approximately 8.165.

Explanation

First, find the square root of 8/3, which is approximately 1.633, then multiply by 5: 1.633 x 5 ≈ 8.165.

Well explained 👍

Problem 4

What will be the square root of (8/3 + 1)?

Okay, lets begin

Approximately 1.915.

Explanation

First, compute 8/3 + 1 = 11/3.

Then, find √(11/3) ≈ 1.915.

Well explained 👍

FAQ on Square Root of 8/3

1.What is √(8/3) in its simplest form?

The simplest radical form of √(8/3) is √8/√3, which can be simplified further using rationalization techniques.

2.Is 8/3 a perfect square?

No, 8/3 is not a perfect square as it cannot be expressed as the square of an integer.

3.How do you calculate the square of 8/3?

The square of 8/3 is (8/3) x (8/3) = 64/9.

4.Is 8/3 greater than 2?

5.What is the decimal approximation of √(8/3)?

The decimal approximation of √(8/3) is approximately 1.63299.

Important Glossary for the Square Root of 8/3

  • Square root: The square root is the inverse operation of squaring a number. For example, 4^2 = 16, so √16 = 4.
  • Irrational number: A number that cannot be expressed as a simple fraction, such as √2 or √(8/3).
  • Decimal: A fractional number expressed in base 10, such as 1.63299.
  • Radical: An expression that uses the root symbol (√) to denote roots, such as √8.
  • Perfect square: A number that is the square of an integer, such as 4 (2^2) or 9 (3^2).

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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.