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Last updated on May 26th, 2025

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Square Root of 3/4

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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.

Square Root of 3/4 for Global Students
Professor Greenline from BrightChamps

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.

Professor Greenline from BrightChamps

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
Professor Greenline from BrightChamps

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.

Professor Greenline from BrightChamps

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.

Professor Greenline from BrightChamps

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.

Professor Greenline from BrightChamps

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.

Max Pointing Out Common Math Mistakes

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.

Mistake 1

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Not Simplifying the Fraction First

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It's important to simplify the fraction before taking the square root.

For example, if a fraction like 6/8 is given, simplify it to 3/4 before proceeding with finding its square root.

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Square Root of 3/4 Examples

Ray, the Character from BrightChamps Explaining Math Concepts
Max, the Girl Character from BrightChamps

Problem 1

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

Ray, the Boy Character from BrightChamps Saying "Let’s 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.

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Max, the Girl Character from BrightChamps

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?

Ray, the Boy Character from BrightChamps Saying "Let’s 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.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 3

Calculate √(3/4) x 8.

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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.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 4

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

Ray, the Boy Character from BrightChamps Saying "Let’s 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.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 5

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

Ray, the Boy Character from BrightChamps Saying "Let’s 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.

Max from BrightChamps Praising Clear Math Explanations
Ray Thinking Deeply About Math Problems

FAQ on Square Root of 3/4

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

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2.Mention the factors of 3/4.

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3.Calculate the square of 3/4.

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4.Is 3/4 a prime number?

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5.Is 3/4 a rational number?

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Professor Greenline from BrightChamps

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.

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Max, the Girl Character from BrightChamps

Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.

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