Square Root of 81/25
2026-02-28 12:05 Diff
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Last updated on December 15, 2025

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.

Problem 1

Can you help Max find the area of a square box if its side length is given as √(81/25)?

Okay, lets begin

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.

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Problem 2

A square-shaped track measures 81/25 square meters; if each side is √(81/25), what will be the square meters of half of the track?

Okay, lets begin

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.

Well explained 👍

Problem 3

Calculate √(81/25) x 10.

Okay, lets begin

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.

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Problem 4

What will be the square root of (81/25 + 4)?

Okay, lets begin

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.

Well explained 👍

Problem 5

Find the perimeter of a rectangle if its length ‘l’ is √(81/25) units and the width ‘w’ is 5 units.

Okay, lets begin

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.

Well explained 👍

FAQ on Square Root of 81/25

1.What is √(81/25) in its simplest form?

The prime factorization of 81 is 3 x 3 x 3 x 3, and of 25 is 5 x 5, so the simplest form of √(81/25) = 9/5.

2.Mention the factors of 81 and 25.

Factors of 81 are 1, 3, 9, 27, 81. Factors of 25 are 1, 5, 25.

3.Calculate the square of (81/25).

We get the square of 81/25 by multiplying the number by itself, that is (81/25) x (81/25) = 6561/625.

4.Is 81/25 a rational number?

Yes, 81/25 is a rational number, as it can be expressed as a fraction with integers.

5.81/25 is divisible by?

81/25 is a fraction and not divisible in the typical sense, but both 81 and 25 individually have factors that they are 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.

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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.