Last updated on May 26th, 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.
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.
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:
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.
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.
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.
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.
Can you help Max find the area of a square box if its side length is given as √(3/8)?
The area of the square is 0.140625 square units.
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.
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?
0.1875 square feet
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.
Calculate √(3/8) x 5.
3.06186
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.
What will be the square root of (3+5/8)?
0.935414
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.
Find the perimeter of the rectangle if its length ‘l’ is √(3/8) units and the width ‘w’ is 4 units.
We find the perimeter of the rectangle as 9.224744 units.
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√(3/8) + 4)
= 2 × (0.612372 + 4)
= 2 × 4.612372
= 9.224744 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.