Square Root of 27/3
2026-02-28 06:15 Diff
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Last updated on August 5, 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 various fields such as vehicle design, finance, etc. Here, we will discuss the square root of 27/3.

What is the Square Root of 27/3?

The square root is the inverse of the square of the number. 27/3 simplifies to 9, which is a perfect square. The square root of 9 is expressed in both radical and exponential form. In the radical form, it is expressed as √9, whereas in the exponential form it is expressed as (9)^(1/2). √9 = 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 27/3

For perfect square numbers like 9, the prime factorization method is a straightforward approach. However, for non-perfect squares, the long division and approximation methods are used. Let us now learn the following methods: - Prime factorization method

  • Long division method
  • Approximation method

Square Root of 27/3 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 9 is broken down into its prime factors.

Step 1: Finding the prime factors of 9. Breaking it down, we get 3 x 3.

Step 2: Now we found out the prime factors of 9. The second step is to make pairs of those prime factors. Since 9 is a perfect square, the digits of the number can be grouped in pairs.

Therefore, calculating √9 using prime factorization, √(3 x 3) = 3.

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Square Root of 27/3 by Long Division Method

The long division method is typically used for non-perfect square numbers, but let's illustrate it with 9 for clarity.

Step 1: To begin with, we need to group the numbers from right to left. In the case of 9, it's a single digit.

Step 2: Now we need to find n whose square is 9. We can say n is ‘3’ because 3 x 3 is equal to 9.

So the square root of √9 is 3.

Square Root of 27/3 by Approximation Method

The approximation method is another approach for finding square roots, especially useful for non-perfect squares. However, for perfect squares like 9, approximation is not needed as the square root is exact. Here, √9 = 3.

Common Mistakes and How to Avoid Them in the Square Root of 27/3

Students do make mistakes while finding the square root, such as forgetting about the negative square root or misunderstanding the simplification process. 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 √(27/3)?

Okay, lets begin

The area of the square is 9 square units.

Explanation

The area of the square = side^2.

The side length is given as √(27/3) = √9 = 3.

Area of the square = side^2 = 3 x 3 = 9.

Therefore, the area of the square box is 9 square units.

Well explained 👍

Problem 2

A square-shaped building measuring 27/3 square feet is built; if each of the sides is √(27/3), what will be the square feet of half of the building?

Okay, lets begin

4.5 square feet

Explanation

We can just divide the given area by 2 as the building is square-shaped.

Dividing 9 by 2, we get 4.5.

So, half of the building measures 4.5 square feet.

Well explained 👍

Problem 3

Calculate √(27/3) x 5.

Okay, lets begin

15

Explanation

The first step is to find the square root of 27/3, which is √9 = 3.

The second step is to multiply 3 with 5.

So, 3 x 5 = 15.

Well explained 👍

Problem 4

What will be the square root of (27/3 + 1)?

Okay, lets begin

The square root is 3.162.

Explanation

To find the square root, we need to find the sum of (27/3 + 1) = 9 + 1 = 10.

The square root of 10 is approximately 3.162.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √(27/3) units and the width ‘w’ is 5 units.

Okay, lets begin

We find the perimeter of the rectangle as 16 units.

Explanation

Perimeter of the rectangle = 2 × (length + width).

Perimeter = 2 × (√(27/3) + 5) = 2 × (3 + 5) = 2 × 8 = 16 units.

Well explained 👍

FAQ on Square Root of 27/3

1.What is √(27/3) in its simplest form?

Since 27/3 simplifies to 9, the simplest form of √(27/3) is √9, which equals 3.

2.Mention the factors of 9.

Factors of 9 are 1, 3, and 9.

3.Calculate the square of 9.

We get the square of 9 by multiplying the number by itself, that is 9 x 9 = 81.

4.Is 9 a prime number?

5.9 is divisible by?

9 is divisible by 1, 3, and 9.

Important Glossaries for the Square Root of 27/3

  • Square root: A square root is the inverse of a square. For example: 3^2 = 9 and the inverse of the square is the square root, so √9 = 3.
  • Rational number: A rational number is a number that can be expressed in the form of p/q, where q is not equal to zero and p and q are integers.
  • Perfect square: A perfect square is an integer that is the square of an integer. For example, 9 is a perfect square because it is 3^2.
  • Prime factorization: Prime factorization is expressing a number as the product of its prime factors. For example, the prime factorization of 9 is 3 x 3.
  • Exponentiation: Exponentiation is a mathematical operation involving two numbers, the base and the exponent. For example, 3^2 means 3 raised to the power of 2, which equals 9.

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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.