122 LearnersLast updated on May 26th, 2025
Square Root of 5/9
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 5/9.
What is the Square Root of 5/9?
The square root is the inverse of the square of the number. 5/9 is not a perfect square. The square root of 5/9 is expressed in both radical and exponential form. In the radical form, it is expressed as, √(5/9), whereas (5/9)^(1/2) in the exponential form. √(5/9) = √5/√9 = √5/3, 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 5/9
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where long-division method and approximation method are used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 5/9 by Prime Factorization Method
The prime factorization of 5 is simply 5, as it is a prime number. The prime factorization of 9 is 3 x 3. Now let us look at how 5/9 is broken down:
Step 1: Finding the prime factors of the numerator and the denominator For 5, we have 5 (as it is prime). For 9, we have 3 x 3.
Step 2: The square root of 5/9 is calculated by taking the square root of the numerator and the denominator separately. √(5/9) = √5/√(3 x 3) = √5/3.
Square Root of 5/9 by Long Division Method
The long division method is particularly used for non-perfect square numbers. Since 5/9 is a fraction, we apply the square root to the numerator and denominator separately:
Step 1: The closest perfect square number to 5 is 4, and for 9, it is 9 itself.
Step 2: Using long division, we can approximate the square root of 5 as 2.236. The square root of 9 is exactly 3.
Step 3: The square root of 5/9 is approximately 2.236/3 = 0.7453.
Square Root of 5/9 by Approximation Method
The approximation method is another method for finding square roots; it is an easy method to find the square root of a given number. Now let us learn how to find the square root of 5/9 using the approximation method.
Step 1: We know the square root of 5 is approximately 2.236 and the square root of 9 is 3.
Step 2: So the square root of 5/9 is approximately 2.236/3 = 0.7453.
Common Mistakes and How to Avoid Them in the Square Root of 5/9
Students do make mistakes while finding the square root, such as forgetting to simplify fractions first. Skipping important steps, etc. Now let us look at a few of those mistakes that students tend to make in detail.
Mistake 1
Forgetting to Simplify Fractions
It is important to simplify fractions before applying operations like square roots. For instance, always reduce fractions to simplest form before proceeding.
Mistake 2
Mixing Up Numerator and Denominator
Ensure students understand the difference between the numerator and the denominator and perform operations on them correctly.
For example, √(5/9) = √5/√9, not √5/√3.
Mistake 3
Not Considering Both Positive and Negative Roots
Remember that a number has both positive and negative square roots. However, in practical applications, we often use only the positive root.
For example: √(5/9) = ±√5/3.
Mistake 4
Incorrectly Applying the Square Root to Fractions
Students may sometimes apply the square root incorrectly across fractions. The square root of a fraction is the square root of the numerator divided by the square root of the denominator.
Mistake 5
Misplacing Decimal Points
When calculating square roots or dividing decimals, ensure the decimal points are correctly placed. This is crucial to obtaining the right value.
Square Root of 5/9 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √(5/9)?
The area of the square is 5/9 square units.
Explanation
The area of the square = side^2.
The side length is given as √(5/9).
Area of the square = (√(5/9))^2
= 5/9.
Therefore, the area of the square box is 5/9 square units.
Problem 2
A square-shaped building measuring 5/9 square feet is built; if each of the sides is √(5/9), what will be the square feet of half of the building?
5/18 square feet
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 5/9 by 2, we get 5/18.
So half of the building measures 5/18 square feet.
Problem 3
Calculate √(5/9) x 5.
3.7265
Explanation
The first step is to find the square root of 5/9, which is approximately 0.7453.
The second step is to multiply 0.7453 with 5.
So 0.7453 x 5 = 3.7265.
Problem 4
What will be the square root of (5 + 4/9)?
The square root is approximately 2.291.
Explanation
To find the square root, we need to find the sum of (5 + 4/9).
5 + 4/9 = 49/9. Then √(49/9) = √49/√9 = 7/3 = 2.333.
Therefore, the square root of (5 + 4/9) is approximately 2.333.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √(5/9) units and the width ‘w’ is 3 units.
We find the perimeter of the rectangle as 6.4906 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√(5/9) + 3)
= 2 × (0.7453 + 3)
= 2 × 3.7453
= 6.4906 units.
FAQ on Square Root of 5/9
1.What is √(5/9) in its simplest form?
2.What are the prime factors of 9?
3.Calculate the square of 5/9.
4.Is 5/9 a perfect square?
5.What is the decimal equivalent of √(5/9)?
6.How does learning Algebra help students in Bahrain make better decisions in daily life?
7.How can cultural or local activities in Bahrain support learning Algebra topics such as Square Root of 5/9?
8.How do technology and digital tools in Bahrain support learning Algebra and Square Root of 5/9?
9.Does learning Algebra support future career opportunities for students in Bahrain?
Important Glossaries for the Square Root of 5/9
- Square root: A square root is the inverse of a square. For example, 4^2 = 16 and the inverse of the square is the square root, that is √16 = 4.
- Irrational number: An irrational number is a number that cannot be written in the form of 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, more generally, any number of equal parts, for example, 5/9.
- Numerator and Denominator: In a fraction, the numerator is the top number and the denominator is the bottom number. In 5/9, 5 is the numerator and 9 is the denominator.
- Decimal: A decimal number is a number that consists of a whole number and a fractional part separated by a decimal point, for example, 0.7453.
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About BrightChamps in Bahrain
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.
