Last updated on May 26th, 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.
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.
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
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.
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.
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.
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.
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.
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.
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
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.
Calculate √(27/3) x 5.
15
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.
What will be the square root of (27/3 + 1)?
The square root is 3.162.
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.
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.
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√(27/3) + 5) = 2 × (3 + 5) = 2 × 8 = 16 units.
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.
: He loves to play the quiz with kids through algebra to make kids love it.