125 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)?
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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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.
