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 the field of vehicle design, finance, etc. Here, we will discuss 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.
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:
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.
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.
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.
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.
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.
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
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.
Calculate 5 times the square root of 7/9.
Approximately 4.4096
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.
What will be the square root of (7/9 + 2/9)?
The square root is 1.
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.
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.
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√(7/9) + 1)
Perimeter ≈ 2 × (0.88192 + 1)
Perimeter ≈ 2 × 1.88192
≈ 3.76384 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.
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