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Last updated on May 26th, 2025

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Square Root of 1/36

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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.

Square Root of 1/36 for Indian Students
Professor Greenline from BrightChamps

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

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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.

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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.

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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

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Forgetting about the negative square root

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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.

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Square root of 1/36 Examples

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Max, the Girl Character from BrightChamps

Problem 1

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

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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.

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Max, the Girl Character from BrightChamps

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?

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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.

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Max, the Girl Character from BrightChamps

Problem 3

Calculate √(1/36) × 5.

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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.

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Max, the Girl Character from BrightChamps

Problem 4

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

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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.

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Max, the Girl Character from BrightChamps

Problem 5

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

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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?

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2.Mention the factors of 36.

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3.Calculate the square of 1/6.

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4.Is 1/36 a rational number?

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

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6.How does learning Algebra help students in India make better decisions in daily life?

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7.How can cultural or local activities in India support learning Algebra topics such as Square Root of 1/36?

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8.How do technology and digital tools in India support learning Algebra and Square Root of 1/36?

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9.Does learning Algebra support future career opportunities for students in India?

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Professor Greenline from BrightChamps

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.
Professor Greenline from BrightChamps

About BrightChamps in India

At BrightChamps, we see algebra as more than just symbols—it opens doors to endless opportunities! Our mission is to help children all over India develop vital math skills, focusing today on the Square Root of 1/36 with special attention to understanding square roots—in a way that’s engaging, lively, and easy to follow. Whether your child is calculating the speed of a passing train, keeping scores during a cricket match, or managing pocket money for the latest gadgets, mastering algebra gives them the confidence needed for everyday situations. Our interactive lessons keep learning simple and fun. As kids in India have varied learning styles, we personalize our approach to match each child. From the busy markets of Mumbai to Delhi’s vibrant streets, BrightChamps brings math to life, making it relatable and exciting throughout India. Let’s make square roots a joyful part of every child’s math journey!
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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.

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Max, the Girl Character from BrightChamps

Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.

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