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130 LearnersLast updated on December 15, 2025
Square Root of 81/25
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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 81/25.
What is the Square Root of 81/25?
The square root is the inverse of the square of the number.
81/25 is a perfect square because both the numerator and the denominator are perfect squares.
The square root of 81/25 is expressed in both radical and exponential form.
In radical form, it is expressed as √(81/25), whereas (81/25)(1/2) in exponential form.
√(81/25) = 9/5, 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 81/25
For perfect square numbers like 81/25, we can use the prime factorization method, as well as direct calculation.
Let us now learn the following methods:
- Prime factorization method
- Direct calculation method
Square Root of 81/25 by Prime Factorization Method
The product of prime factors is the prime factorization of a number.
Now let us look at how 81 and 25 are broken down into their prime factors:
Step 1: Finding the prime factors of 81 and 25 81 = 3 x 3 x 3 x 3 = 34, 25 = 5 x 5 = 52
Step 2: Now, we find the square root by taking the square roots of the numerator and denominator separately. √(34) = 32 = 9 √(52) = 5
So, √(81/25) = 9/5.
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Square Root of 81/25 by Direct Calculation Method
The direct calculation method is straightforward for perfect squares.
In this method, we directly take the square roots of the numerator and denominator:
Step 1: Take the square root of the numerator, which is 81. √81 = 9
Step 2: Take the square root of the denominator, which is 25. √25 = 5
Step 3: Divide the square root of the numerator by the square root of the denominator. 9/5 = 1.8
Thus, the square root of 81/25 is 9/5 or 1.8.
Approximation Method for Non-Perfect Squares
The approximation method is generally used for non-perfect squares, but since 81/25 is a perfect square, its square root is exact.
For example, if you had a non-perfect square like 82/25, you would find the closest perfect squares and use them to approximate the square root.
Common Mistakes and How to Avoid Them in Finding the Square Root of 81/25
Students do make mistakes while finding the square root, like forgetting whether the number is a perfect square or not. Skipping direct calculation methods, etc.
Now let us look at a few of those mistakes that students tend to make in detail.
Mistake 1
Forgetting about Rational Numbers
It is important to make students aware that a number can be a rational number if it can be expressed as a fraction.
For example, the square root of 81/25 is 9/5, which is rational.
Mistake 2
Not Simplifying the Fraction First
Sometimes, students forget to simplify fractions first.
Ensure that you simplify fractions before taking square roots to make calculations easier.
Mistake 3
Not Finding the Correct Value for Non-Perfect Squares
The first step that needs to be taught to children is to simplify the numbers inside the square root.
For non-perfect squares, approximation techniques are required.
Mistake 4
Confusing the Square Root Symbol
Students need to be clear about the use of the square root symbol and not confuse it with other operations, such as division or multiplication.
Mistake 5
Making Mistakes in Prime Factorization
Finding a square root using prime factorization involves identifying correct pairs of factors, which can sometimes be skipped, leading to errors.
Square Root of 81/25 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as โ(81/25)?
The area of the square is 3.24 square units.
Explanation
The area of the square = side².
The side length is given as √(81/25), which is 9/5 or 1.8.
Area of the square = side² = (9/5) x (9/5) = 1.8 x 1.8 = 3.24
Therefore, the area of the square box is 3.24 square units.
Problem 2
A square-shaped track measures 81/25 square meters; if each side is โ(81/25), what will be the square meters of half of the track?
1.62 square meters
Explanation
We can just divide the given area by 2 as the track is square-shaped.
Dividing 3.24 by 2 = we get 1.62
So half of the track measures 1.62 square meters.
Problem 3
Calculate โ(81/25) x 10.
18
Explanation
The first step is to find the square root of 81/25, which is 1.8.
The second step is to multiply 1.8 with 10.
So 1.8 x 10 = 18.
Problem 4
What will be the square root of (81/25 + 4)?
The square root is 3.
Explanation
To find the square root, we need to find the sum of (81/25 + 4). 81/25 = 3.24, and 3.24 + 4 = 7.24
However, rewriting the expression as a fraction, (81/25 + 100/25) = 181/25, and √(181/25) is approximately 3.
Therefore, the square root of (81/25 + 4) is approximately ±3.
Problem 5
Find the perimeter of a rectangle if its length โlโ is โ(81/25) units and the width โwโ is 5 units.
We find the perimeter of the rectangle as 13.6 units.
Explanation
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√(81/25) + 5) = 2 × (1.8 + 5) = 2 × 6.8 = 13.6 units.
FAQ on Square Root of 81/25
1.What is โ(81/25) in its simplest form?
2.Mention the factors of 81 and 25.
3.Calculate the square of (81/25).
4.Is 81/25 a rational number?
5.81/25 is divisible by?
Important Glossaries for the Square Root of 81/25
- Square root: A square root is the inverse of a square. Example: 4² = 16, and the inverse of the square is the square root, 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.
- Principal square root: A number has both positive and negative square roots; however, it is always the positive square root that is more prominent due to its uses in the real world. That is why it is also known as the principal square root.
- Perfect square: A perfect square is a number that is the square of an integer. For example, 81 is a perfect square because it is 9².
- Fraction: A fraction represents a part of a whole or a division of quantities. For example, 81/25 is a fraction.
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.
