Last updated on May 26th, 2025
If a number is multiplied by itself, the result is a square. The inverse of the square is the square root. The square root has applications in fields like vehicle design, finance, and more. Here, we will discuss the square root of 7/2.
The square root is the inverse of the square of a number. 7/2 is not a perfect square. The square root of 7/2 is expressed in both radical and exponential form. In the radical form, it is expressed as √(7/2), whereas in exponential form, it is expressed as (7/2)^(1/2). √(7/2) = 1.8708, 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.
We can find the square root of a fraction by finding the square roots of the numerator and the denominator separately. For non-perfect square numbers, approximation methods can be used. Let us now learn the following methods:
1. Simplification method
2. Approximation method
The simplification method involves finding the square roots of the numerator and the denominator separately.
Step 1: Find the square root of the numerator 7. Since 7 is not a perfect square, we approximate √7 ≈ 2.64575.
Step 2: Find the square root of the denominator 2. √2 ≈ 1.41421.
Step 3: Combine the results: √(7/2) = √7 / √2 ≈ 2.64575 / 1.41421 ≈ 1.8708.
The approximation method is straightforward and involves estimating the square root numerically.
Step 1: Estimate √7 ≈ 2.64575 and √2 ≈ 1.41421.
Step 2: Divide the estimates: 2.64575 / 1.41421 ≈ 1.8708.
Step 3: Therefore, the square root of 7/2 is approximately 1.8708.
Students often make mistakes while calculating square roots, such as neglecting the negative square root or mishandling fractions. Let's explore some common mistakes.
Can you help Max find the area of a square box if its side length is given as √(3.5)?
The area of the square is 3.5 square units.
The area of a square = side^2.
The side length is given as √(3.5).
Area of the square = side^2 = √(3.5) × √(3.5) = 3.5.
Therefore, the area of the square box is 3.5 square units.
A rectangle has an area of 7/2 square feet. If its length is √(7/2), what will be the square feet of half of the rectangle?
1.75 square feet
We can divide the given area by 2 since the area is 7/2 square feet.
Dividing 7/2 by 2 = 7/4 = 1.75
So half of the rectangle measures 1.75 square feet.
Calculate √(7/2) × 10.
18.708
The first step is to find the square root of 7/2, which is approximately 1.8708.
The second step is to multiply 1.8708 by 10.
So 1.8708 × 10 = 18.708.
What will be the square root of (7 + 1)?
The square root is 2.82843.
To find the square root, we need to find the sum of (7 + 1). 7 + 1 = 8, and then √8 ≈ 2.82843.
Therefore, the square root of (7 + 1) is ±2.82843.
Find the perimeter of a rectangle if its length ‘l’ is √(7/2) units and the width ‘w’ is 5 units.
The perimeter of the rectangle is approximately 13.7416 units.
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√(7/2) + 5) = 2 × (1.8708 + 5) = 2 × 6.8708 = 13.7416 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.
: He loves to play the quiz with kids through algebra to make kids love it.