105 LearnersLast updated on May 26th, 2025
Square Root of 1/36
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.
What is 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.
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Finding the Square Root of 1/36
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
Square Root of 1/36 by 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.
Square Root of 1/36 by Long Division Method
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.
Square Root of 1/36 by Approximation 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.
Common Mistakes and How to Avoid Them in the Square Root of 1/36
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.
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 will be taking only the positive square root, as it is the required one.
For example: √(1/36) = 1/6, there is also -1/6 which should not be forgotten.
Mistake 2
Not adding square root symbol in proper places
Not using the square root properly is another mistake that children make. To resolve this, we need to teach children that simplifying the numbers inside the square root is important, and then move on to the second step.
For example: √(9/36) = 3/6 is the right method of using roots.
Mistake 3
Not finding the correct value of a non-perfect square
The first step that needs to be taught to children is to simplify the numbers inside the square root. This is important so that students do not make mistakes while identifying the approximate value.
For example: √50 = 7 is wrong; the correct answer is √50 ≈ 7.071067.
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, √50 and ∛50 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 sum. This may either happen in subtracting or elsewhere.
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Square root of 1/36 Examples
Problem 1
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.
Explanation
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.
Problem 2
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
Explanation
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.
Problem 3
Calculate √(1/36) × 5.
5/6
Explanation
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.
Problem 4
What will be the square root of (1/36 + 1/36)?
The square root is 1/√18.
Explanation
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.
Problem 5
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.
Explanation
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.
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FAQ on Square Root of 1/36
1.What is √(1/36) in its simplest form?
2.Mention the factors of 36.
3.Calculate the square of 1/6.
4.Is 1/36 a rational number?
5.What is the inverse of the square root of 1/36?
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Important Glossaries for the Square Root of 1/36
- Square root: A square root is the inverse of a square. Example: 4^2 = 16, and the inverse of the square is the square root, that is √16 = 4.
- Rational number: A rational number is a number that can be written in the form of p/q, q is not equal to zero, and p and q are integers.
- Perfect square: A perfect square is a number that is the square of an integer. For example, 36 is a perfect square because it is 6^2.
- Reciprocal: The reciprocal of a number is 1 divided by that number. For example, the reciprocal of 6 is 1/6.
- Prime factorization: Breaking down a number into its basic building blocks or prime factors. For example, the prime factorization of 36 is 2 × 2 × 3 × 3.
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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.
