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 the field of vehicle design, finance, etc. Here, we will discuss the square root of 1/36.
The square root is the inverse of the square of the number. 1/36 is a perfect square. The square root of 1/36 is expressed in both radical and exponential form. In the radical form, it is expressed as √(1/36), whereas (1/36)^(1/2) is the exponential form. √(1/36) = 1/6, 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.
The prime factorization method is used for perfect square numbers. Since 1/36 is a perfect square, we can use the prime factorization method directly. 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 1/36 is broken down into its prime factors.
Step 1: Finding the prime factors of 36 Breaking it down, we get 2 × 2 × 3 × 3: 2^2 × 3^2
Step 2: Since 1 is already a perfect square (1 × 1), we only need to consider the square root of 36. The square root of 36 is 6. Therefore, the square root of 1/36 is 1/6.
The long division method is generally used for non-perfect square numbers. However, since 1/36 is a perfect square, we can directly compute its square root without using the long division method.
Since 1/36 is a perfect square, the approximation method is not necessary. The exact value of the square root of 1/36 is 1/6.
Students do make mistakes while finding the square root, like forgetting about the negative square root. Skipping methods, etc. Now let us look at a few of those mistakes that students tend to make in detail.
Can you help Max find the side length of a square box if its area is 1/36 square units?
The side length of the square is 1/6 units.
The side length of a square = √(area).
The area is given as 1/36.
Therefore, side length = √(1/36) = 1/6.
The side length of the square box is 1/6 units.
A square-shaped garden measures 1/36 square meters; if each of the sides is √(1/36), what will be the square meters of half of the garden?
1/72 square meters
We can just divide the given area by 2 as the garden is square-shaped.
Dividing 1/36 by 2 = we get 1/72.
So, half of the garden measures 1/72 square meters.
Calculate √(1/36) × 5.
5/6
The first step is to find the square root of 1/36, which is 1/6, the second step is to multiply 1/6 with 5.
So, 1/6 × 5 = 5/6.
What will be the square root of (1/36 + 1/36)?
The square root is 1/√18.
To find the square root, we need to find the sum of (1/36 + 1/36).
1/36 + 1/36 = 2/36 = 1/18, and then √(1/18).
Therefore, the square root of (1/36 + 1/36) is ±1/√18.
Find the perimeter of a rectangle if its length ‘l’ is √(1/36) units and the width ‘w’ is 1/3 units.
We find the perimeter of the rectangle as 5/6 units.
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√(1/36) + 1/3) = 2 × (1/6 + 1/3) = 2 × (1/6 + 2/6) = 2 × 3/6 = 2 × 1/2 = 1.
Therefore, the perimeter is 1 unit.
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.