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135 LearnersLast updated on December 15, 2025
Square Root of 9/25
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 fields such as vehicle design, finance, etc. Here, we will discuss the square root of 9/25.
What is the Square Root of 9/25?
The square root is the inverse of the square of a number. 9/25 is a perfect square.
The square root of 9/25 can be expressed in both radical and exponential form.
In radical form, it is expressed as √(9/25), whereas in exponential form it is (9/25)(1/2).
√(9/25) = √9/√25 = 3/5, which is a rational number because it can be expressed in the form of p/q, where p and q are integers and q ≠ 0.
Finding the Square Root of 9/25
The prime factorization method can be used for finding the square root of perfect square numbers, like 9/25.
However, other methods such as the long division method and approximation method are not needed in this case.
Let's learn how to find the square root of 9/25 using the prime factorization method:
- Prime factorization method
- Rationalization method
- Approximation method
Square Root of 9/25 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Let us look at how 9/25 is broken down into its prime factors:
Step 1: Finding the prime factors of 9 and 25 9 can be broken down as 3 x 3: 32 25 can be broken down as 5 x 5: 52
Step 2: Now we have found out the prime factors of both 9 and 25. Since both 9 and 25 are perfect squares, we can take the square root of each: √(9/25) = √9/√25 = 3/5
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Square Root of 9/25 by Rationalization Method
The rationalization method is particularly used for perfect square fractions.
In this method, we take the square root of the numerator and the square root of the denominator separately.
Let us now learn how to find the square root using this method, step by step:
Step 1: Take the square root of the numerator: √9 = 3
Step 2: Take the square root of the denominator: √25 = 5
Step 3: The square root of the fraction is the quotient of these square roots: √(9/25) = 3/5
Square Root of 9/25 by Approximation Method
The approximation method is not necessary for finding the square root of 9/25, as it is a perfect square fraction.
However, if needed, we would look at the closest perfect square fractions and use them to approximate.
In this case, we directly find the square root as 3/5.
Common Mistakes and How to Avoid Them in the Square Root of 9/25
Students often make mistakes while finding the square root, such as forgetting about the negative square root or misapplying the square root to the numerator or denominator.
Here are a few common mistakes and how to avoid them.
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 usually take only the positive square root unless specified otherwise.
For example: √(9/25) = ±3/5.
Mistake 2
Incorrectly applying the square root
Sometimes students incorrectly apply the square root only to the numerator or the denominator, rather than both.
Ensure that the square root is applied to both parts of the fraction: √(9/25) = √9/√25.
Mistake 3
Confusing square roots with cube roots
Students need to be aware of the difference between square roots and cube roots.
For example, √(9/25) and โ(9/25) are different.
Mistake 4
Not simplifying correctly
Sometimes students fail to simplify the square root correctly.
Ensure the simplified result is expressed as a fraction: √(9/25) = 3/5.
Mistake 5
Misunderstanding the properties of square roots
Understanding that the square root of a quotient is the quotient of the square roots is crucial: √(a/b) = √a/√b, where a and b are non-negative.
Square Root of 9/25 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as โ(9/25)?
The area of the square is 9/25 square units.
Explanation
The area of the square = side2.
The side length is given as √(9/25).
Area of the square = side2 = (3/5) x (3/5) = 9/25.
Therefore, the area of the square box is 9/25 square units.
Problem 2
A square-shaped building measuring 9/25 square meters is built; if each of the sides is โ(9/25), what will be the square meters of half of the building?
4.5/25 square meters
Explanation
We can just divide the given area by 2 as the building is square-shaped.
Dividing 9/25 by 2 = we get 4.5/25.
So half of the building measures 4.5/25 square meters.
Problem 3
Calculate โ(9/25) x 5.
3
Explanation
First, find the square root of 9/25, which is 3/5.
The second step is to multiply 3/5 by 5.
So 3/5 x 5 = 3.
Problem 4
What will be the square root of (9/25 + 16/25)?
The square root is 1.
Explanation
To find the square root, we need to find the sum of (9/25 + 16/25). 9/25 + 16/25 = 25/25 = 1, and then √1 = 1.
Therefore, the square root of (9/25 + 16/25) is ±1.
Problem 5
Find the perimeter of the rectangle if its length โlโ is โ(9/25) units and the width โwโ is 3 units.
We find the perimeter of the rectangle as 13/5 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√(9/25) + 3) = 2 × (3/5 + 15/5) = 2 × 18/5 = 36/5 units.
FAQ on Square Root of 9/25
1.What is โ(9/25) in its simplest form?
2.Mention the factors of 9/25.
3.Calculate the square of 9/25.
4.Is 9/25 a rational number?
5.9/25 is divisible by?
Important Glossaries for the Square Root of 9/25
- Square root: A square root is the inverse of a square. Example: 42 = 16 and the inverse of the square is the square root which is √16 = 4.
- Rational number: A rational number is a number that can be written in the form of p/q, where q is not equal to zero and p and q are integers.
- Perfect square: A number that is the square of an integer. For example, 9 and 25 are perfect squares.
- Fraction: A fraction consists of a numerator and a denominator and represents a part of a whole.
- Prime factorization: Breaking down a number into its prime factors. For example, the prime factorization of 9 is 3 x 3.
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.
