Square Root of 3/4
2026-02-28 17:28 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 like vehicle design, finance, etc. Here, we will discuss the square root of 3/4.

What is the Square Root of 3/4?

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

Since 3/4 is a fraction, we use the property of square roots that allows us to take the square root of the numerator and the denominator separately. Let us now learn the following methods:

  • Prime factorization method
  • Simplification method
  • Numerical approximation method

Square Root of 3/4 by Simplification Method

The simplification method allows us to find the square root of a fraction by taking the square root of the numerator and the denominator separately. Step 1: The numerator is 3, and the denominator is 4. Step 2: Take the square root of each part separately: √3 and √4. Step 3: The square root of 4 is 2, as 2 x 2 = 4. Step 4: Therefore, the square root of 3/4 is √3/2.

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Square Root of 3/4 by Numerical Approximation

Numerical approximation is a method used to find a more precise decimal value for the square root of a number.

Step 1: Approximate the square root of the numerator, √3 ≈ 1.732.

Step 2: The square root of the denominator, √4, is 2.

Step 3: Divide the approximate square root of the numerator by the exact square root of the denominator: 1.732/2 = 0.866.

Square Root of 3/4 by Prime Factorization Method

The prime factorization method is generally used for whole numbers, but it can help us understand the properties of the square roots involved.

Step 1: Prime factorization of 3 is itself, as it's a prime number.

Step 2: Prime factorization of 4 is 2 x 2.

Step 3: As we cannot form complete pairs for 3, it indicates the result will be irrational.

Comparison with Whole Number Square Roots

It is useful to compare the value of √(3/4) with the square roots of whole numbers to understand its relative size.

Step 1: We know √1 = 1, which is greater than 0.866.

Step 2: Therefore, √(3/4) ≈ 0.866 is less than 1 but greater than √0.

Common Mistakes and How to Avoid Them in the Square Root of 3/4

Students often make mistakes while finding the square root of fractions, such as not simplifying the fraction beforehand or confusing numerator and denominator. Now let us look at a few of those mistakes in detail.

Problem 1

Can you help Max find the area of a square box if its side length is given as √(3/4)?

Okay, lets begin

The area of the square is 0.75 square units.

Explanation

The area of the square = side^2.

The side length is given as √(3/4).

Area of the square = (√(3/4))^2 = 3/4 = 0.75.

Therefore, the area of the square box is 0.75 square units.

Well explained 👍

Problem 2

A square-shaped garden measures 3/4 square feet; if each of the sides is √(3/4), what will be the square feet of half of the garden?

Okay, lets begin

0.375 square feet

Explanation

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

Dividing 3/4 by 2 = we get 3/8 = 0.375.

So half of the garden measures 0.375 square feet.

Well explained 👍

Problem 3

Calculate √(3/4) x 8.

Okay, lets begin

6.928

Explanation

The first step is to find the square root of 3/4, which is approximately 0.866.

The second step is to multiply 0.866 by 8.

So 0.866 x 8 = 6.928.

Well explained 👍

Problem 4

What will be the square root of (3/4 + 1/4)?

Okay, lets begin

The square root is 1.

Explanation

To find the square root, we need to find the sum of (3/4 + 1/4) 3/4 + 1/4 = 1, and then √1 = 1.

Therefore, the square root of (3/4 + 1/4) is 1.

Well explained 👍

Problem 5

Find the perimeter of a rectangle if its length ‘l’ is √(3/4) units and the width ‘w’ is 1 unit.

Okay, lets begin

The perimeter of the rectangle is 3.732 units.

Explanation

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

Perimeter = 2 × (√(3/4) + 1) = 2 × (0.866 + 1) = 2 × 1.866 = 3.732 units.

Well explained 👍

FAQ on Square Root of 3/4

1.What is √(3/4) in its simplest form?

The simplest form of √(3/4) is √3/2.

2.Mention the factors of 3/4.

3.Calculate the square of 3/4.

We get the square of 3/4 by multiplying the number by itself, that is (3/4) x (3/4) = 9/16.

4.Is 3/4 a prime number?

No, 3/4 is a fraction, and the concept of prime numbers applies only to whole numbers.

5.Is 3/4 a rational number?

Yes, 3/4 is a rational number because it can be expressed as a fraction of two integers, with a non-zero denominator.

Important Glossaries for the Square Root of 3/4

  • Square root: A square root is the inverse of a square. Example: 4^2 = 16, and the inverse of the square is the square root that is √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.
  • Fraction: A fraction represents a part of a whole or, more generally, any number of equal parts. It consists of a numerator and a denominator.
  • Numerical approximation: This is a method of finding an approximate value of a number, often used for square roots to find a decimal representation.
  • Simplification: Simplification involves reducing a mathematical expression or fraction to its simplest form.

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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.