Square Root of 3/8
2026-02-28 06:05 Diff
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Last updated on August 5, 2025

If a number is multiplied by itself, the result is a square. The inverse of the square is a square root. The square root is used in fields such as vehicle design, finance, etc. Here, we will discuss the square root of 3/8.

What is the Square Root of 3/8?

The square root is the inverse of the square of a number. The fraction 3/8 is not a perfect square. The square root of 3/8 is expressed in both radical and exponential forms. In the radical form, it is expressed as √(3/8), whereas (3/8)^(1/2) in the exponential form. √(3/8) = √3/√8 = √3/(2√2) which simplifies to √6/4. 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 3/8

Various methods can be used to find the square root of fractions or non-perfect square numbers, such as the long-division method and approximation method. Let us now learn the following methods:

  • Simplifying the radical
  • Long division method
  • Approximation method

Square Root of 3/8 by Simplifying the Radical

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

Step 1: Find the square root of the numerator and the denominator separately: √3 and √8.

Step 2: Simplify the expression: √(3/8) = √3/√8.

Step 3: Multiply the numerator and denominator by √2 to rationalize the denominator: √3/√8 = √3/(2√2) = √6/4.

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Square Root of 3/8 by Long Division Method

The long division method is particularly useful for approximating square roots of non-perfect squares. In this method, we should check the closest perfect square number for the given fraction.

Step 1: Convert 3/8 into decimal form: 3 divided by 8 is 0.375.

Step 2: Use the long division method to find the square root of 0.375 (as we would for any decimal number).

Step 3: Continue the division process until you reach the desired precision.

The approximate square root of 0.375 is 0.612372.

Square Root of 3/8 by Approximation Method

The approximation method is another method for finding square roots, and it is an easy method to find the square root of a given number. Now let us learn how to find the square root of 3/8 using the approximation method.

Step 1: Convert 3/8 into decimal form: 0.375.

Step 2: Find two perfect squares that 0.375 lies between. For example, 0.25 (0.5^2) and 0.36 (0.6^2).

Step 3: Use interpolation to approximate the square root: 0.375 is closer to 0.36, so the square root is closer to 0.6.

Step 4: Using interpolation, approximate √0.375 as approximately 0.612.

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

Students often make mistakes while finding the square root, such as forgetting to rationalize the denominator or incorrectly converting fractions to decimals. 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 √(3/8)?

Okay, lets begin

The area of the square is 0.140625 square units.

Explanation

The area of the square = side^2.

The side length is given as √(3/8).

Area of the square = (√(3/8))^2

= 3/8

= 0.375

Therefore, the area of the square box is 0.375 square units.

Well explained 👍

Problem 2

A square-shaped building measuring 3/8 square feet is built; if each of the sides is √(3/8), what will be the square feet of half of the building?

Okay, lets begin

0.1875 square feet

Explanation

We can just divide the given area by 2 as the building is square-shaped.

Dividing 3/8 by 2 = we get 3/16 = 0.1875.

So half of the building measures 0.1875 square feet.

Well explained 👍

Problem 3

Calculate √(3/8) x 5.

Okay, lets begin

3.06186

Explanation

First, find the square root of 3/8, which is approximately 0.612372, then multiply it by 5.

So, 0.612372 x 5 = 3.06186.

Well explained 👍

Problem 4

What will be the square root of (3+5/8)?

Okay, lets begin

0.935414

Explanation

First, find the sum of (3 + 5/8). 3 + 5/8 = 3.625, then find the square root of 3.625, which is approximately 1.903.

Therefore, the square root of (3+5/8) is approximately 1.903.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √(3/8) units and the width ‘w’ is 4 units.

Okay, lets begin

We find the perimeter of the rectangle as 9.224744 units.

Explanation

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

Perimeter = 2 × (√(3/8) + 4)

= 2 × (0.612372 + 4)

= 2 × 4.612372

= 9.224744 units.

Well explained 👍

FAQ on Square Root of 3/8

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

2.Calculate the square of 3/8.

We get the square of 3/8 by multiplying the number by itself, that is (3/8) x (3/8) = 9/64.

3.Is 3/8 a perfect square?

3/8 is not a perfect square because it cannot be expressed as the square of a rational number.

4.How do you convert 3/8 into decimal form?

To convert 3/8 into decimal form, divide 3 by 8 to get 0.375.

5.What is the reciprocal of 3/8?

The reciprocal of 3/8 is 8/3.

Important Glossaries for the Square Root of 3/8

  • Square root: A square root is the inverse of a square. For example, 4^2 = 16 and the inverse of the square is the square root, so √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.
     
  • Decimal: If a number has a whole number and a fraction in a single number, it is called a decimal. For example, 7.86, 8.65, and 9.42 are decimals.
     
  • Rationalize: Rationalizing is the process of eliminating the square root or cube root from the denominator of a fraction.
     
  • Fraction: A fraction represents a part of a whole and is expressed as a ratio of two numbers, such as 3/8.

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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.