148 LearnersLast updated on May 26th, 2025
Square Root of 3/4
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.
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.
Mistake 1
Not Simplifying the Fraction First
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.
Mistake 2
Mixing the Numerator and Denominator
Students sometimes confuse which part of the fraction to apply the square root to, leading to errors. Remember, apply the square root separately to both the numerator and the denominator.
Mistake 3
Forgetting about the Irrationality of Square Roots
Students often overlook that the square root of non-perfect squares, like 3, results in an irrational number. Ensure students understand that √3 is not a simple fraction.
Mistake 4
Confusing Square Roots with Reciprocals
Some students mistakenly think that finding the square root of a fraction involves taking reciprocals. Emphasize that the square root is different from finding the reciprocal.
Mistake 5
Errors in Numerical Approximation
When approximating square roots, students might round off too early, leading to inaccuracies. It's important to maintain precision during calculations.
Square Root of 3/4 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √(3/4)?
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.
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?
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.
Problem 3
Calculate √(3/4) x 8.
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.
Problem 4
What will be the square root of (3/4 + 1/4)?
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.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √(3/4) units and the width ‘w’ is 1 unit.
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.
FAQ on Square Root of 3/4
1.What is √(3/4) in its simplest form?
2.Mention the factors of 3/4.
3.Calculate the square of 3/4.
4.Is 3/4 a prime number?
5.Is 3/4 a rational number?
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.
