130 LearnersLast updated on May 26th, 2025
Square Root of 9/5
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 9/5.
What is the Square Root of 9/5?
The square root is the inverse of the square of the number. 9/5 is not a perfect square. The square root of 9/5 is expressed in both radical and exponential form. In radical form, it is expressed as √(9/5), whereas (9/5)^(1/2) in exponential form. √(9/5) = √9/√5 = 3/√5 = 3√5/5, 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 9/5
The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers such as fractions, where rationalizing the denominator is often used. Let us now learn the following methods:
- Rationalizing the denominator
- Decimal approximation
Square Root of 9/5 by Rationalizing the Denominator
Rationalizing the denominator involves converting a fraction with a square root in the denominator into an equivalent fraction with a rational denominator.
Step 1: Identify the square root in the denominator. Here, it is √5.
Step 2: Multiply both the numerator and the denominator by √5 to eliminate the square root from the denominator. (3/√5) × (√5/√5) = (3√5)/5
Step 3: Now, the expression is rationalized, with the square root remaining only in the numerator.
Square Root of 9/5 by Decimal Approximation
Decimal approximation is another method for finding square roots, and it is useful for estimating the value.
Step 1: Calculate the decimal form of 9/5, which is 1.8.
Step 2: Find the square root of 1.8 using a calculator or estimation, which is approximately 1.3416.
Mistakes to Avoid When Finding the Square Root of 9/5
Students often make mistakes when working with square roots, especially with fractions. Here are some common mistakes and how to avoid them:
Forgetting to Rationalize the Denominator
When dealing with square roots of fractions, it's crucial to rationalize the denominator.For instance, leaving the answer as 3/√5 without rationalizing would be incorrect in some contexts. Always multiply by the conjugate to rationalize.
Common Mistakes and How to Avoid Them in the Square Root of 9/5
Students do make mistakes while finding the square root, like forgetting to rationalize the denominator or ignoring the negative square root. Skipping steps in calculation can also lead to errors. Now let us look at a few of those mistakes that students tend to make in detail.
Mistake 1
Forgetting about the Negative Square Root
It is important to remember that a number has both positive and negative square roots. However, we typically take only the positive square root in practical applications.
For example: √(9/5) = 1.3416, but there is also -1.3416, which should not be forgotten in theoretical contexts.
Mistake 2
Not Rationalizing the Denominator Properly
Another common mistake is failing to rationalize the denominator. To resolve this, ensure you multiply the numerator and the denominator by the square root present in the denominator.
For example, (3/√5) should be rationalized to (3√5)/5.
Mistake 3
Confusing the Process with Taking Sqrt of Numerator and Denominator Separately
Students might mistakenly take the square root of the numerator and denominator separately without considering the fraction as a whole.
For example, √(9/5) is not the same as √9/√5 if you don't simplify correctly.
Mistake 4
Mistakes in Decimal Approximation
When approximating, make sure to use a calculator or a reliable method to find the square root to avoid errors.
For example, approximating √1.8 without a calculator might lead to inaccuracies.
Mistake 5
Overlooking the Fact that the Result is Irrational
It's crucial to understand that the square root of non-perfect squares is often irrational. Students should be aware that √(9/5) is irrational, meaning it can't be expressed as a simple fraction.
Square Root of 9/5 Examples
Problem 1
Can you help Max find the area of a square if its side length is given as √(9/5)?
The area of the square is approximately 1.8 square units.
Explanation
The area of the square = side².
The side length is given as √(9/5).
Area of the square = side²
= (√(9/5))²
= 9/5
= 1.8.
Therefore, the area of the square is 1.8 square units.
Problem 2
A square-shaped park measuring 9/5 square units is created. If each of the sides is √(9/5), what will be the total length of the boundary of the park?
Approximately 5.3664 units.
Explanation
The perimeter of a square = 4 × side.
Side length = √(9/5)
≈ 1.3416.
Perimeter = 4 × 1.3416
≈ 5.3664 units.
Problem 3
Calculate √(9/5) × 10.
Approximately 13.416.
Explanation
First, find the square root of 9/5, which is approximately 1.3416.
Then, multiply 1.3416 by 10.
So, 1.3416 × 10 ≈ 13.416.
Problem 4
What will be the square root of (45/25)?
The square root is 3/5.
Explanation
To find the square root, we need to simplify (45/25) to (9/5).
Then, √(9/5) = 3/√5 = 3√5/5.
Therefore, the square root of (45/25) is 3/5.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √(9/5) units and the width ‘w’ is 5 units.
The perimeter of the rectangle is approximately 12.6832 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√(9/5) + 5)
Perimeter = 2 × (1.3416 + 5)
Perimeter ≈ 2 × 6.3416
≈ 12.6832 units.
FAQ on Square Root of 9/5
1.What is √(9/5) in its simplest form?
2.Is 9/5 a perfect square?
3.What is the decimal approximation of √(9/5)?
4.Does √(9/5) have a negative value?
5.Can you express √(9/5) as a fraction?
6.How does learning Algebra help students in Qatar make better decisions in daily life?
7.How can cultural or local activities in Qatar support learning Algebra topics such as Square Root of 9/5?
8.How do technology and digital tools in Qatar support learning Algebra and Square Root of 9/5?
9.Does learning Algebra support future career opportunities for students in Qatar?
Important Glossaries for the Square Root of 9/5
- Square root: A square root is the inverse of a square. For example, 4² = 16, and the inverse of the square is the square root, which 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.
- Rationalizing the denominator: The process of eliminating a square root from the denominator of a fraction by multiplying both the numerator and denominator by an appropriate value.
- Decimal approximation: An estimated value of a number that cannot be precisely expressed as a simple fraction but is represented in decimal form.
- Fraction: A mathematical expression representing the division of one integer by another. For example, 9/5 is a fraction.
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About BrightChamps in Qatar
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.
