Square Root of 1/36
2026-02-28 06:21 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1/36

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Last updated on August 5, 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.

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.

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.

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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.

Problem 1

Can you help Max find the side length of a square box if its area is 1/36 square units?

Okay, lets begin

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.

Well explained 👍

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?

Okay, lets begin

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.

Well explained 👍

Problem 3

Calculate √(1/36) × 5.

Okay, lets begin

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.

Well explained 👍

Problem 4

What will be the square root of (1/36 + 1/36)?

Okay, lets begin

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.

Well explained 👍

Problem 5

Find the perimeter of a rectangle if its length ‘l’ is √(1/36) units and the width ‘w’ is 1/3 units.

Okay, lets begin

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.

Well explained 👍

FAQ on Square Root of 1/36

1.What is √(1/36) in its simplest form?

The prime factorization of 36 is 2 × 2 × 3 × 3, so the simplest form of √(1/36) = 1/6.

2.Mention the factors of 36.

Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.

3.Calculate the square of 1/6.

We get the square of 1/6 by multiplying the number by itself, that is, (1/6) × (1/6) = 1/36.

4.Is 1/36 a rational number?

Yes, 1/36 is a rational number because it can be expressed as a fraction of two integers.

5.What is the inverse of the square root of 1/36?

The inverse of the square root of 1/36 is 6, because the reciprocal of 1/6 is 6.

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.