Last updated on May 26th, 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.
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.
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:
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.
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.
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.
Can you help Max find the area of a square box if its side length is given as √(1/8)?
The area of the square is 1/8 square units.
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.
A square-shaped plot measures 1/8 of a square meter. What is the side length of the plot?
The side length of the plot is √(1/8) meters.
For a square plot, the side length is the square root of the area. Side length = √(1/8) meters.
Calculate √(1/8) × 4.
The result is √2/2 or approximately 1.4142.
First, find the square root of 1/8, which is √2/4.
Then multiply by 4. (√2/4) × 4 = √2.
What is the square root of (1/4 + 1/8)?
The square root is √(3/8).
First, find the sum: 1/4 + 1/8 = 2/8 + 1/8 = 3/8.
Then, take the square root: √(3/8).
Find the perimeter of a rectangle if its length ‘l’ is √(1/8) units and the width ‘w’ is 1 unit.
The perimeter of the rectangle is approximately 2.7071 units.
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√(1/8) + 1)
= 2 × (0.35355 + 1)
≈ 2.7071 units.
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.
: He loves to play the quiz with kids through algebra to make kids love it.