Square Root of 3/7
2026-02-28 06:08 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-3/7

298 Learners

Last updated on August 5, 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.

What is 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.

Finding the Square Root of 3/7

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:

  • Long division method
  • Approximation method

Square Root of 3/7 by Long Division Method

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.

Explore Our Programs

Square Root of 3/7 by Approximation Method

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.

Common Mistakes and How to Avoid Them in the Square Root of 3/7

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.

Problem 1

Can you help find the area of a square box if its side length is given as √(3/7)?

Okay, lets begin

The area of the square is approximately 0.428 square units.

Explanation

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.

Well explained 👍

Problem 2

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?

Okay, lets begin

0.214 square meters

Explanation

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.

Well explained 👍

Problem 3

Calculate √(3/7) x 5.

Okay, lets begin

Approximately 3.27325

Explanation

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.

Well explained 👍

Problem 4

What will be the square root of (3/7 + 1)?

Okay, lets begin

The square root is approximately 1.1547

Explanation

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.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length 'l' is √(3/7) units and the width 'w' is 2 units.

Okay, lets begin

The perimeter of the rectangle is approximately 5.3093 units.

Explanation

Perimeter of the rectangle = 2 × (length + width).

Perimeter = 2 × (√(3/7) + 2)

≈ 2 × (0.65465 + 2)

= 2 × 2.65465

≈ 5.3093 units.

Well explained 👍

FAQ on Square Root of 3/7

1.What is √(3/7) in its simplest form?

The fraction 3/7 is already in its simplest form, so √(3/7) is expressed as √3/√7.

2.How do you find the square root of a fraction?

To find the square root of a fraction, find the square roots of the numerator and the denominator separately, and then divide them.

3.Calculate the square of 3/7.

The square of 3/7 is (3/7) x (3/7) = 9/49.

4.Is 3/7 a rational number?

Yes, 3/7 is a rational number because it can be expressed as a fraction where both the numerator and the denominator are integers.

5.3/7 is divisible by?

3/7 itself is a fraction, and fractions are not divisible like whole numbers.

You can simplify it only if both the numerator and the denominator share a common factor.

Important Glossaries for the Square Root of 3/7

  • Square root: A square root is the inverse of a square. Example: 4² = 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 and is expressed as p/q where p and q are integers and q ≠ 0.
     
  • Rational number: A rational number can be expressed as a fraction where both the numerator and the denominator are integers.
     
  • Approximation method: A technique used to find an estimated value of a square root, especially for non-perfect squares.

What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math

▶

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.