121 LearnersLast updated on May 26th, 2025
Square Root of 8/9
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 various fields such as engineering, finance, etc. Here, we will discuss the square root of 8/9.
What is 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.
Finding the Square Root of 8/9
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
Square Root of 8/9 by Simplification 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.
Square Root of 8/9 by Decimal Approximation Method
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.
Common Mistakes and How to Avoid Them in the Square Root of 8/9
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.
Mistake 1
Forgetting to Simplify the Fraction
It is crucial to simplify the fraction before finding its square root when possible. For example, if the fraction can be reduced, do so before taking the square root. Simplification can lead to easier calculations and more accurate results.
Mistake 2
Not Finding the Square Root of Both Numerator and Denominator
Ensure you take the square root of both the numerator and the denominator separately.
For example, √(8/9) should be calculated as √8/√9, not simply √8/9.
Mistake 3
Incorrectly Converting to Decimal
When converting a fraction to a decimal, ensure that you divide correctly. Misplacing the decimal point or dividing incorrectly can lead to errors in the final result.
Mistake 4
Confusing Square Root with Square
Remember that a square root is not the same as squaring a number. For example, √(8/9) is not the same as (8/9)^2. Ensure you apply the correct operation.
Mistake 5
Rounding Errors in Decimal Approximation
When using the decimal approximation method, be aware of rounding errors. Ensure you round to an appropriate number of decimal places to maintain accuracy in your calculations.
Square Root of 8/9 Examples
Problem 1
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.
Explanation
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.
Problem 2
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
Explanation
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.
Problem 3
Calculate √(8/9) x 5.
4.71405
Explanation
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.
Problem 4
What will be the square root of (8/9 + 1/9)?
The square root is 1.
Explanation
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.
Problem 5
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.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√(8/9) + 1)
= 2 × (0.94281 + 1)
= 2 × 1.94281
= 3.88562 units.
FAQ on Square Root of 8/9
1.What is √(8/9) in its simplest form?
2.Can the square root of 8/9 be expressed as a fraction?
3.Calculate the square of 8/9.
4.Is 8/9 a perfect square?
5.What are the factors of 8/9?
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 8/9?
8.How do technology and digital tools in Australia support learning Algebra and Square Root of 8/9?
9.Does learning Algebra support future career opportunities for students in Australia?
Important Glossaries for the Square Root of 8/9
- Square root: A square root is the inverse of a square. For example, 3² = 9, and the inverse of the square is the square root, so √9 = 3.
- Rational number: A rational number is a number that can be expressed in the form p/q, where q is not equal to zero and p and q are integers.
- Fraction: A fraction represents a part of a whole or any number of equal parts. It is expressed as a/b, where a is the numerator and b is the denominator.
- Decimal: A decimal is a way of expressing numbers that include a whole number and a fraction, represented with a decimal point. For example, 0.5, 0.75, and 1.25 are decimals.
- Perfect square: A perfect square is a number that is the square of an integer. For example, 9 is a perfect square because it is 3².
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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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