127 LearnersLast updated on May 26th, 2025
Square Root of 27/3
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.
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.
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 typically take only the positive square root in practical applications.
For example: √9 = 3, but there is also -3 which should not be forgotten.
Mistake 2
Not adding square root symbols in proper places
Not using the square root symbol properly is another mistake that students make. To resolve this, we need to teach students that simplifying the numbers inside the square root is important and then move on to the second step.
For example: √(4 + 5) = √9 is correct, not √4 + √5.
Mistake 3
Not finding the correct value of a non-perfect square
The first step that needs to be taught to students is to simplify the numbers inside the square root. This is important so that students do not make mistakes while identifying the value.
For example: √10 is approximately 3.162, not 3.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between cube root and square root constantly, as this will help them avoid mistakes.
For example: √9 and ∛9 are different.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves many steps. Due to this, many students might skip a step accidentally, which results in a wrong answer at the end of the calculation.
Square Root of 27/3 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √(27/3)?
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.
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?
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.
Problem 3
Calculate √(27/3) x 5.
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.
Problem 4
What will be the square root of (27/3 + 1)?
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.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √(27/3) units and the width ‘w’ is 5 units.
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.
FAQ on Square Root of 27/3
1.What is √(27/3) in its simplest form?
2.Mention the factors of 9.
3.Calculate the square of 9.
4.Is 9 a prime number?
5.9 is divisible by?
6.How does learning Algebra help students in Philippines make better decisions in daily life?
7.How can cultural or local activities in Philippines support learning Algebra topics such as Square Root of 27/3?
8.How do technology and digital tools in Philippines support learning Algebra and Square Root of 27/3?
9.Does learning Algebra support future career opportunities for students in Philippines?
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
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