Square Root of 7/9
2026-02-28 06:06 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-7/9

240 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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 7/9.

What is the Square Root of 7/9?

The square root is the inverse of the square of the number. The number 7/9 is not a perfect square. The square root of 7/9 is expressed in both radical and exponential form. In radical form, it is expressed as √(7/9), whereas (7/9)^(1/2) in exponential form. √(7/9) = √7/√9 = √7/3, 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 7/9

The prime factorization method is typically used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers; instead, methods like simplification and approximation are employed. Let us now learn the following methods:

  • Simplification method
  • Approximation method

Square Root of 7/9 by Simplification Method

The simplification method involves expressing the fraction as a product of its individual square roots.

Step 1: Express the fraction as individual square roots. √(7/9) = √7/√9

Step 2: Simplify the square root of the denominator. Since √9 = 3, we have √(7/9) = √7/3

Step 3: The value √7 remains under the square root as it is not a perfect square.

Therefore, the simplified form of √(7/9) is √7/3.

Explore Our Programs

Square Root of 7/9 by Approximation Method

The approximation method is another approach for finding the square roots. It is an easy method to estimate the square root of a given number. Now let us learn how to approximate the square root of 7/9.

Step 1: Approximate the square root of the numerator and denominator separately. The square root of 7 is approximately 2.64575. The square root of 9 is exactly 3.

Step 2: Divide the approximate square root of the numerator by the exact square root of the denominator. 2.64575 ÷ 3 ≈ 0.88192

Therefore, the approximate value of √(7/9) is around 0.88192.

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

▶

Common Mistakes and How to Avoid Them in the Square Root of 7/9

Students often make mistakes while finding the square root, such as forgetting about the negative square root, skipping simplification steps, etc. Now let us look at a few of those mistakes that students tend to make in detail.

Problem 1

Can you help Max find the side length of a square if its area is given as 7/9 square units?

Okay, lets begin

The side length of the square is approximately 0.88192 units.

Explanation

The side length of a square is the square root of its area.

The area of the square is 7/9 square units.

Side length = √(7/9) ≈ 0.88192

Therefore, the side length of the square is approximately 0.88192 units.

Well explained 👍

Problem 2

A square-shaped garden measures 7/9 square meters in area. If each side of the garden is √(7/9) meters, what will be the area of half of the garden?

Okay, lets begin

0.3889 square meters

Explanation

To find the area of half of the garden, we can divide the total area by 2.

7/9 ÷ 2 = 7/18

Therefore, half of the garden measures 7/18 or approximately 0.3889 square meters.

Well explained 👍

Problem 3

Calculate 5 times the square root of 7/9.

Okay, lets begin

Approximately 4.4096

Explanation

First, find the square root of 7/9, which is approximately 0.88192.

Multiply this value by 5. 0.88192 × 5 ≈ 4.4096

Therefore, 5 times the square root of 7/9 is approximately 4.4096.

Well explained 👍

Problem 4

What will be the square root of (7/9 + 2/9)?

Okay, lets begin

The square root is 1.

Explanation

First, find the sum of (7/9 + 2/9).

7/9 + 2/9 = 9/9 = 1

Then, find the square root of 1. √1 = ±1

Therefore, the square root of (7/9 + 2/9) is ±1.

Well explained 👍

Problem 5

Find the perimeter of a rectangle if its length 'l' is √(7/9) units and the width 'w' is 1 unit.

Okay, lets begin

The perimeter of the rectangle is approximately 3.76384 units.

Explanation

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

Perimeter = 2 × (√(7/9) + 1)

Perimeter ≈ 2 × (0.88192 + 1)

Perimeter ≈ 2 × 1.88192

≈ 3.76384 units.

Well explained 👍

FAQ on Square Root of 7/9

1.What is √(7/9) in its simplest form?

The simplest form of √(7/9) is √7/3, since the square root of 9 is 3, and the numerator remains under the square root.

2.What are the factors of 7/9?

The factors of the fraction 7/9 are 7 and 9. In terms of whole numbers, the factors of 7 are 1 and 7, and the factors of 9 are 1, 3, and 9.

3.Calculate the square of 7/9.

We get the square of 7/9 by multiplying the fraction by itself: (7/9) × (7/9) = 49/81.

4.Is 7/9 a rational number?

Yes, 7/9 is a rational number, as it can be expressed as a fraction where both the numerator and the denominator are integers.

5.What is the reciprocal of 7/9?

The reciprocal of 7/9 is 9/7.

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.