121 LearnersLast updated on May 26th, 2025
Square Root of 7/9
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.
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.
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.
Mistake 1
Forgetting about the negative square root
It is important to make students aware that a number has both positive and negative square roots. However, we will usually consider only the positive square root unless specified otherwise.
For example, the square root of 7/9 is ±√7/3.
Mistake 2
Not simplifying the fraction before finding the square root
A common mistake is to find the square root without simplifying the fraction first. It is crucial to simplify the fraction, if possible, before finding the square root.
For example, √(14/18) should be simplified to √(7/9).
Mistake 3
Confusing square roots with cube roots
Students need to be consistently reminded of the difference between cube roots and square roots to avoid confusion.
For example, the square root of 7/9 is √(7/9), whereas the cube root would be ∛(7/9).
Mistake 4
Misplacing the square root symbol
Students sometimes place the square root symbol incorrectly. Ensure that the square root encompasses the entire expression where necessary.
For example, √(7/9) should not be written as √7/9.
Mistake 5
Errors in approximation
When using approximation, students may make errors in the calculation, leading to incorrect values. Practice and attention to detail can help avoid these errors.
Square Root of 7/9 Examples
Problem 1
Can you help Max find the side length of a square if its area is given as 7/9 square units?
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.
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?
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.
Problem 3
Calculate 5 times the square root of 7/9.
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.
Problem 4
What will be the square root of (7/9 + 2/9)?
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.
Problem 5
Find the perimeter of a rectangle if its length 'l' is √(7/9) units and the width 'w' is 1 unit.
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.
FAQ on Square Root of 7/9
1.What is √(7/9) in its simplest form?
2.What are the factors of 7/9?
3.Calculate the square of 7/9.
4.Is 7/9 a rational number?
5.What is the reciprocal of 7/9?
6.How does learning Algebra help students in Australia make better decisions in daily life?
7.How can cultural or local activities in Australia support learning Algebra topics such as Square Root of 7/9?
8.How do technology and digital tools in Australia support learning Algebra and Square Root of 7/9?
9.Does learning Algebra support future career opportunities for students in Australia?
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Jaskaran Singh Saluja
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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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