Last updated on May 26th, 2025
If a number is multiplied by itself, the result is a square. The inverse of squaring a number is finding its square root. Square roots are used in various fields such as vehicle design, finance, etc. Here, we will discuss 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.
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:
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.
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.
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.
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.
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.
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.
The side length of the square is the square root of its area.
Therefore, the side length is √(7/4) ≈ 1.322875 meters.
Calculate √(7/4) × 3.
The result is approximately 3.968625.
First, find the square root of 7/4, which is approximately 1.322875.
Then multiply this by 3: 1.322875 × 3 ≈ 3.968625.
What will be the result of the expression 2 × √(7/4)?
The result is approximately 2.645751.
To solve the expression, multiply 2 by the square root of 7/4.
√(7/4) ≈ 1.322875, so 2 × 1.322875 ≈ 2.645751.
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.
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.
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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