Square Root of 1/8
2026-02-28 06:08 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1/8

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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 squaring a number is finding its square root. Square roots are used in various fields such as engineering, finance, and physics. Here, we will discuss the square root of 1/8.

What is the Square Root of 1/8?

The square root is the inverse operation of squaring a number. 1/8 is a fraction, and its square root can be expressed in both radical and exponential form. In radical form, it is expressed as √(1/8), whereas in exponential form it is (1/8)^(1/2). The value of √(1/8) is approximately 0.35355, which is an irrational number because it cannot be expressed as a simple fraction of integers.

Finding the Square Root of 1/8

For fractions, the square root can be found directly. However, for non-perfect squares, approximation methods may be used. Let us now discuss the following methods:

  • Direct calculation method
  • Approximation method

Square Root of 1/8 by Direct Calculation

To find the square root of a fraction like 1/8, you can take the square roots of the numerator and the denominator separately:

Step 1: Square root of the numerator: √1 = 1

Step 2: Square root of the denominator: √8 = √(4 × 2) = 2√2

Step 3: Combine the results: √(1/8) = 1/(2√2)

Step 4: Simplify if necessary: Multiply numerator and denominator by √2 to rationalize the denominator: 1/(2√2) × √2/√2 = √2/4

Thus, the square root of 1/8 is √2/4.

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Square Root of 1/8 by Approximation Method

The approximation method can be used to find the square root of a fraction. For √(1/8), we first convert it to a decimal and then find its square root.

Step 1: Convert 1/8 to a decimal: 1/8 = 0.125

Step 2: Use a calculator or estimate the square root of 0.125, which is approximately 0.35355.

Therefore, the approximate square root of 1/8 is 0.35355.

Common Mistakes and How to Avoid Them in Finding the Square Root of 1/8

Students often make errors while finding square roots, such as misunderstanding the properties of fractions or failing to rationalize denominators. Let's look at a few common mistakes in detail.

Problem 1

Can you help Max find the area of a square box if its side length is given as √(1/8)?

Okay, lets begin

The area of the square is 1/8 square units.

Explanation

The area of the square = side².

The side length is given as √(1/8).

Area of the square = (√(1/8))²

= 1/8.

Therefore, the area of the square box is 1/8 square units.

Well explained 👍

Problem 2

A square-shaped plot measures 1/8 of a square meter. What is the side length of the plot?

Okay, lets begin

The side length of the plot is √(1/8) meters.

Explanation

For a square plot, the side length is the square root of the area. Side length = √(1/8) meters.

Well explained 👍

Problem 3

Calculate √(1/8) × 4.

Okay, lets begin

The result is √2/2 or approximately 1.4142.

Explanation

First, find the square root of 1/8, which is √2/4.

Then multiply by 4. (√2/4) × 4 = √2.

Well explained 👍

Problem 4

What is the square root of (1/4 + 1/8)?

Okay, lets begin

The square root is √(3/8).

Explanation

First, find the sum: 1/4 + 1/8 = 2/8 + 1/8 = 3/8.

Then, take the square root: √(3/8).

Well explained 👍

Problem 5

Find the perimeter of a rectangle if its length ‘l’ is √(1/8) units and the width ‘w’ is 1 unit.

Okay, lets begin

The perimeter of the rectangle is approximately 2.7071 units.

Explanation

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

Perimeter = 2 × (√(1/8) + 1)

= 2 × (0.35355 + 1)

≈ 2.7071 units.

Well explained 👍

FAQ on Square Root of 1/8

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

√(1/8) can be expressed as √2/4 in its simplest form.

2.Is 1/8 a perfect square?

1/8 is not a perfect square because it cannot be expressed as the square of a rational number.

3.What is the decimal value of √(1/8)?

The decimal value of √(1/8) is approximately 0.35355.

4.How do you rationalize the denominator of √(1/8)?

To rationalize the denominator of √(1/8), you multiply by √2/√2, resulting in √2/4.

5.Is √(1/8) an irrational number?

Yes, √(1/8) is an irrational number because it cannot be expressed as a simple fraction of integers.

Important Glossaries for the Square Root of 1/8

  • Square root: A square root is a value that, when multiplied by itself, gives the original number. For example, √4 = 2 because 2 × 2 = 4.
     
  • Rationalization: Rationalization is the process of eliminating a radical from the denominator of a fraction.
     
  • Irrational number: An irrational number cannot be expressed as a simple fraction, such as √2.
     
  • Fraction: A fraction represents a part of a whole and consists of a numerator and a denominator.
     
  • Decimal: A decimal is a number that includes a decimal point to represent a fraction, such as 0.5, which is equivalent to 1/2.

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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.