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378 LearnersLast updated on August 5, 2025
Square Root of 7/4
What is the Square Root of 7/4?
The square root is the inverse operation of squaring a number. 7/4 is not a perfect square. The square root of 7/4 can be expressed in both radical and exponential forms. In radical form, it is expressed as √(7/4), whereas in exponential form as (7/4)^(1/2). √(7/4) is approximately equal to 1.322875, which is an irrational number because it cannot be expressed as a fraction p/q, where p and q are integers and q ≠ 0.
Finding the Square Root of 7/4
The square root of fractions is usually found using simpler methods since the prime factorization method is more suited to whole numbers. For non-perfect square fractions, methods like simplification and approximation are used. Let us explore these methods:
- Simplification method
- Approximation method
Square Root of 7/4 by Simplification Method
The simplification method is used to simplify the square root of a fraction. Let us see how to find the square root of 7/4 using this method:
Step 1: Express the fraction as a division of square roots: √(7/4) = √7 / √4.
Step 2: Simplify the denominator: √4 = 2.
Step 3: The expression becomes √7 / 2, which is approximately 1.322875.
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Square Root of 7/4 by Approximation Method
The approximation method helps in estimating the square root of a given number or fraction. Let's learn how to approximate the square root of 7/4.
Step 1: Find the square root of the numerator (7) and denominator (4) separately. √7 is approximately 2.645751, and √4 is 2.
Step 2: Divide the results: √7 / √4 = 2.645751 / 2 = 1.322875.
Thus, √(7/4) is approximately 1.322875.
Common Mistakes and How to Avoid Them in the Square Root of 7/4
Students often make mistakes when finding square roots, such as overlooking the negative square root. Let's look at some common mistakes and how to avoid them.
Square Root of 7/4 Examples
Problem 1
Can you help Max find the hypotenuse of a right triangle if one side is √(7/4) and the other side is 1?
The hypotenuse of the triangle is approximately 1.658312 units.
Explanation
To find the hypotenuse, use the Pythagorean theorem: c = √(a² + b²).
Here, a = √(7/4) ≈ 1.322875 and b = 1.
c = √((1.322875)² + 1²) = √(1.75 + 1) = √2.75 ≈ 1.658312.
Problem 2
A square field has an area of 7/4 square meters. What is the side length of the field?
The side length of the field is approximately 1.322875 meters.
Explanation
The side length of the square is the square root of its area.
Therefore, the side length is √(7/4) ≈ 1.322875 meters.
Problem 3
Calculate √(7/4) × 3.
The result is approximately 3.968625.
Explanation
First, find the square root of 7/4, which is approximately 1.322875.
Then multiply this by 3: 1.322875 × 3 ≈ 3.968625.
Problem 4
What will be the result of the expression 2 × √(7/4)?
The result is approximately 2.645751.
Explanation
To solve the expression, multiply 2 by the square root of 7/4.
√(7/4) ≈ 1.322875, so 2 × 1.322875 ≈ 2.645751.
Problem 5
Find the perimeter of a rectangle if its length 'l' is √(7/4) units and the width 'w' is 2 units.
The perimeter of the rectangle is approximately 6.64575 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Here, length = √(7/4) ≈ 1.322875 and width = 2.
Perimeter = 2 × (1.322875 + 2) = 2 × 3.322875 ≈ 6.64575 units.
FAQ on Square Root of 7/4
1.What is √(7/4) in its simplest form?
2.Is 7/4 a perfect square?
3.How do you calculate the square of 7/4?
4.Is 7/4 a rational number?
5.Is the square root of 7/4 rational or irrational?
Important Glossaries for the Square Root of 7/4
- Square root: The square root is the inverse operation of squaring a number. For example, if 4² = 16, then √16 = 4.
- Irrational number: An irrational number cannot be precisely expressed as a fraction of two integers. For example, √2 and π are irrational numbers.
- Rational number: A rational number can be expressed as a fraction where both the numerator and denominator are integers, and the denominator is not zero.
- Fraction: A fraction is a numerical quantity that is not a whole number, represented by two numbers, a numerator and a denominator.
- Approximation: The process of finding an estimate that is close to the exact value, often used when dealing with irrational numbers or complex calculations.
Vikrant Sharma
About the Author
Vikrant Sharma 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.
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