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 engineering, finance, etc. Here, we will discuss the square root of 8/9.
The square root is the inverse of the square of a number. 8/9 is a fraction, and its square root can be expressed in both radical and exponential forms. In radical form, it is expressed as √(8/9), whereas in exponential form, it is (8/9)^(1/2). The square root of 8/9 simplifies to √8/√9, which is approximately 0.94281. This is a rational number because it can be expressed as a fraction.
To find the square root of a fraction, you can take the square root of the numerator and the square root of the denominator separately. Let us now learn the following methods: Simplification method Decimal approximation method
To simplify the square root of a fraction like 8/9, follow these steps:
Step 1: Find the square root of the numerator and the denominator separately. The numerator is 8, and the denominator is 9.
Step 2: The square root of 8 is approximately 2.82843, and the square root of 9 is exactly 3.
Step 3: Divide the square root of the numerator by the square root of the denominator: 2.82843/3 = 0.94281.
Thus, the square root of 8/9 is approximately 0.94281.
The decimal approximation method for finding the square root is straightforward. Here is how you can find the square root of 8/9 using this method:
Step 1: Convert the fraction 8/9 into a decimal, which is approximately 0.88889.
Step 2: Use a calculator to find the square root of 0.88889, which is approximately 0.94281.
Students often make mistakes while finding the square root, such as forgetting to simplify the fraction or incorrectly applying the square root to both the numerator and the denominator separately. Here are some common mistakes and how to avoid them.
Can you help Max find the area of a square box if its side length is given as √(8/9)?
The area of the square is 0.88889 square units.
The area of the square = side².
The side length is given as √(8/9).
Area of the square = (√(8/9))²
= 8/9
= 0.88889.
Therefore, the area of the square box is 0.88889 square units.
A square-shaped building measuring 8/9 square feet is built; if each of the sides is √(8/9), what will be the square feet of half of the building?
0.44444 square feet
We can just divide the given area by 2 as the building is square-shaped.
Dividing 8/9 by 2 = (8/9)/2
= 0.44444.
So half of the building measures 0.44444 square feet.
Calculate √(8/9) x 5.
4.71405
The first step is to find the square root of 8/9, which is approximately 0.94281.
The second step is to multiply 0.94281 by 5. So 0.94281 x 5 = 4.71405.
What will be the square root of (8/9 + 1/9)?
The square root is 1.
To find the square root, first find the sum of (8/9 + 1/9).
8/9 + 1/9 = 9/9 = 1, and then √1 = 1.
Therefore, the square root of (8/9 + 1/9) is 1.
Find the perimeter of the rectangle if its length 'l' is √(8/9) units and the width 'w' is 1 unit.
The perimeter of the rectangle is 3.88562 units.
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√(8/9) + 1)
= 2 × (0.94281 + 1)
= 2 × 1.94281
= 3.88562 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.