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Last updated on May 26th, 2025

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Square Root of 27/3

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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.

Square Root of 27/3 for Bahraini Students
Professor Greenline from BrightChamps

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.

Professor Greenline from BrightChamps

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
Professor Greenline from BrightChamps

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.

Professor Greenline from BrightChamps

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.

Professor Greenline from BrightChamps

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.

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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.

Mistake 1

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Forgetting about the negative square root

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It is important to make students aware that a number does have both positive and negative square roots. However, we typically take only the positive square root in practical applications.

For example: √9 = 3, but there is also -3 which should not be forgotten.

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Square Root of 27/3 Examples

Ray, the Character from BrightChamps Explaining Math Concepts
Max, the Girl Character from BrightChamps

Problem 1

Can you help Max find the area of a square box if its side length is given as √(27/3)?

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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.

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Max, the Girl Character from BrightChamps

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?

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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.

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Max, the Girl Character from BrightChamps

Problem 3

Calculate √(27/3) x 5.

Ray, the Boy Character from BrightChamps Saying "Let’s 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.

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Max, the Girl Character from BrightChamps

Problem 4

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

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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.

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Max, the Girl Character from BrightChamps

Problem 5

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

Ray, the Boy Character from BrightChamps Saying "Let’s 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.

Max from BrightChamps Praising Clear Math Explanations
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FAQ on Square Root of 27/3

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

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2.Mention the factors of 9.

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3.Calculate the square of 9.

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4.Is 9 a prime number?

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5.9 is divisible by?

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6.How does learning Algebra help students in Bahrain make better decisions in daily life?

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7.How can cultural or local activities in Bahrain support learning Algebra topics such as Square Root of 27/3?

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8.How do technology and digital tools in Bahrain support learning Algebra and Square Root of 27/3?

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9.Does learning Algebra support future career opportunities for students in Bahrain?

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Professor Greenline from BrightChamps

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.
Professor Greenline from BrightChamps

About BrightChamps in Bahrain

At BrightChamps, we understand algebra as more than symbols—it’s a gateway to countless opportunities! We are dedicated to helping children across Bahrain master essential math skills, focusing today on the Square Root of 27/3 with special attention to square roots—in a fun, lively, and easy-to-follow manner. Whether your child is figuring out the speed of a roller coaster at Bahrain’s Wahooo! Waterpark, following local football scores, or managing their allowance to buy the latest gadgets, mastering algebra builds confidence for daily challenges. Our hands-on lessons make learning simple and enjoyable. Because kids in Bahrain learn differently, we customize our teaching to fit each learner’s style. From Manama’s lively city life to peaceful beaches, BrightChamps brings math to life, making it exciting throughout Bahrain. Let’s make square roots a fun part of every child’s math journey!
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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.

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Max, the Girl Character from BrightChamps

Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.

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