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127 LearnersLast updated on December 15, 2025
Square Root of 9/100
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 9/100.
What is the Square Root of 9/100?
The square root is the inverse of the square of the number. 9/100 is a perfect square.
The square root of 9/100 can be expressed in both radical and fractional form.
In the radical form, it is expressed as √(9/100), whereas, in fractional form, it is (3/10).
√(9/100) = 0.3, 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 9/100
The prime factorization method is often used for perfect square numbers.
Let's learn how to find the square root of a fraction using the following methods:
- Prime factorization method
- Simplification method
Square Root of 9/100 by Prime Factorization Method
The product of prime factors is the prime factorization of a number.
Now let us look at how 9/100 is broken down into its prime factors:
Step 1: Finding the prime factors of 9 and 100.
Breaking them down, we get 3 x 3 for 9 and 2 x 2 x 5 x 5 for 100.
Step 2: We found out the prime factors of 9 and 100. The next step is to take the square root of each number. Since 9 is 3 x 3, its square root is 3. Since 100 is 2 x 2 x 5 x 5, its square root is 10.
Therefore, the square root of 9/100 is 3/10 or 0.3.
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Square Root of 9/100 by Simplification Method
The simplification method is particularly useful for perfect square fractions.
In this method, we find the square root of the numerator and denominator separately.
Let us now learn how to find the square root using the simplification method, step by step:
Step 1: Identify the square root of the numerator, which is √9 = 3.
Step 2: Identify the square root of the denominator, which is √100 = 10.
Step 3: Express the square root of the fraction as the fraction of the square roots: √(9/100) = 3/10.
Thus, the square root of 9/100 is 0.3.
Square Root of 9/100 by Approximation Method
The approximation method is not necessary here since 9/100 is a perfect square.
However, if it were not, we would find the closest perfect squares and approximate the value.
Here, the exact square root is 0.3, calculated directly from the prime factorization or simplification methods.
Common Mistakes and How to Avoid Them in the Square Root of 9/100
Students do make mistakes while finding the square root, such as forgetting about the negative square root or incorrectly simplifying fractions.
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 make students aware that a number does have both positive and negative square roots.
However, we will be taking only the positive square root, as it is the required one.
For example: √(9/100) = 0.3, there is also -0.3 which should not be forgotten.
Mistake 2
Not adding the square root symbol in proper places
Not using the square root properly is another mistake that children make.
To resolve this, we need to teach children that simplifying the numbers inside the square root is important and then move on to the second step.
For example: √(3/9) = √3/√9 is a correct method of simplifying roots.
Mistake 3
Not finding the correct value of a non-perfect square
The first step that needs to be taught to children is to simplify the numbers inside the square root.
This is important so that students do not make mistakes while identifying the approximate value.
For Example: √(10/100) = 0.32 is an approximation, not an exact value.
Mistake 5
Making mistakes in simplification
Finding a square root involves the simplification of the fraction.
Due to this, many students might skip a step accidentally, which results in a wrong answer at the end of the sum.
This may happen while dividing the numerator and the denominator by their greatest common divisor.
Square Root of 9/100 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as โ(9/100)?
The area of the square is 0.09 square units.
Explanation
The area of the square = side².
The side length is given as √(9/100).
Area of the square = side² = √(9/100) x √(9/100) = 0.3 × 0.3 = 0.09.
Therefore, the area of the square box is 0.09 square units.
Problem 2
A square-shaped garden measures 9/100 square meters; if each of the sides is โ(9/100), what will be the area of half of the garden?
0.045 square meters
Explanation
We can just divide the given area by 2 as the garden is square-shaped.
Dividing 0.09 by 2 = we get 0.045.
So half of the garden measures 0.045 square meters.
Problem 3
Calculate โ(9/100) x 5.
1.5
Explanation
The first step is to find the square root of 9/100, which is 0.3.
The second step is to multiply 0.3 by 5.
So 0.3 x 5 = 1.5.
Problem 4
What will be the square root of (9/100 + 1/100)?
The square root is 0.316227766
Explanation
To find the square root, we need to find the sum of (9/100 + 1/100).
9/100 + 1/100 = 10/100 = 0.1.
Therefore, the square root of (10/100) is ±0.316227766.
Problem 5
Find the perimeter of the rectangle if its length โlโ is โ(9/100) units and the width โwโ is 0.5 units.
We find the perimeter of the rectangle as 1.6 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√(9/100) + 0.5) = 2 × (0.3 + 0.5) = 2 × 0.8 = 1.6 units.
FAQ on Square Root of 9/100
1.What is โ(9/100) in its simplest form?
2.Mention the factors of 9 and 100.
3.Calculate the square of 9/100.
4.Is 9/100 a prime fraction?
5.9/100 is divisible by?
Important Glossaries for the Square Root of 9/100
- 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, that 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.
- Fraction: A fraction is a part of a whole, represented as a/b, where a is the numerator and b is the denominator.
- Prime factorization: Prime factorization is the process of expressing a number as the product of its prime factors.
- Perfect square: A perfect square is a number that has an integer as its square root. For example, 9 is a perfect square because its square root is 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.
