Last updated on May 26th, 2025
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 such as vehicle design, finance, etc. Here, we will discuss the square root of 3/7.
The square root is the inverse of the square of a number. The fraction 3/7 is not a perfect square. The square root of 3/7 can be expressed in both radical and exponential form. In the radical form, it is expressed as √(3/7), whereas in the exponential form, it is (3/7)^(1/2). The square root of 3/7 is approximately 0.65465, 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.
For non-perfect squares, methods such as the long division method and approximation method are used to find square roots. Let us now learn the following methods:
The long division method is particularly used for non-perfect squares. In this method, we can find the square root of a fraction by finding the square roots of the numerator and denominator separately.
Step 1: Find the square root of the numerator 3 and the denominator 7 separately using the long division method.
Step 2: The approximate square root of 3 is 1.732, and the square root of 7 is 2.646.
Step 3: Divide the square root of the numerator by the square root of the denominator: 1.732 / 2.646 ≈ 0.65465.
So, the square root of 3/7 is approximately 0.65465.
The approximation method is an easy way to find the square root of a given number. Now let us learn how to find the square root of 3/7 using the approximation method.
Step 1: Estimate the square root of the numerator 3, which is between 1 and 2. Similarly, estimate the square root of the denominator 7, which is between 2 and 3.
Step 2: Use the approximation formula to adjust the estimates and divide them to get the square root of the fraction. By approximation, √3 ≈ 1.732 and √7 ≈ 2.646, so √(3/7) ≈ 0.65465.
Students often make mistakes while finding the square root, such as forgetting about the negative square root or failing to simplify fractions correctly. Let's look at a few common mistakes in detail.
Can you help find the area of a square box if its side length is given as √(3/7)?
The area of the square is approximately 0.428 square units.
The area of the square = side^2.
The side length is given as √(3/7).
Area of the square = (√(3/7))^2
= 3/7
≈ 0.428.
Therefore, the area of the square box is approximately 0.428 square units.
A square-shaped garden has an area of 3/7 square meters. If each of the sides is √(3/7), what will be the area of half of the garden?
0.214 square meters
We can just divide the given area by 2 as the garden is square-shaped.
Dividing 3/7 by 2, we get 3/14 ≈ 0.214.
So half of the garden measures approximately 0.214 square meters.
Calculate √(3/7) x 5.
Approximately 3.27325
First, find the square root of 3/7, which is approximately 0.65465.
Then multiply it by 5. So, 0.65465 x 5 ≈ 3.27325.
What will be the square root of (3/7 + 1)?
The square root is approximately 1.1547
To find the square root, first find the sum of (3/7 + 1).
3/7 + 1 = 10/7.
Then √(10/7) ≈ 1.1547.
Therefore, the square root of (3/7 + 1) is approximately ±1.1547.
Find the perimeter of the rectangle if its length 'l' is √(3/7) units and the width 'w' is 2 units.
The perimeter of the rectangle is approximately 5.3093 units.
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√(3/7) + 2)
≈ 2 × (0.65465 + 2)
= 2 × 2.65465
≈ 5.3093 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.