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Last updated on May 26th, 2025

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Square Root of 16/36

Professor Greenline Explaining Math Concepts

If a number is multiplied by the same number, the result is a square. The inverse of a square is a square root. The square root is used in fields such as vehicle design, finance, etc. Here, we will discuss the square root of 16/36.

Square Root of 16/36 for Global Students
Professor Greenline from BrightChamps

What is the Square Root of 16/36?

The square root is the inverse of the square of a number. 16/36 is a perfect square fraction. The square root of 16/36 is expressed in both radical and exponential form. In the radical form, it is expressed as √(16/36), whereas (16/36)^(1/2) in the exponential form. √(16/36) = 2/3, 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.

Professor Greenline from BrightChamps

Finding the Square Root of 16/36

The prime factorization method is used for perfect square numbers. Since 16/36 is a perfect square fraction, we can use the prime factorization method to find its square root. Let us now learn the following methods:

 

  • Prime factorization method
     
  • Long division method
     
  • Approximation method
Professor Greenline from BrightChamps

Square Root of 16/36 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 16/36 is broken down into its prime factors.

 

Step 1: Finding the prime factors of 16 and 36 16 can be broken down into 2 x 2 x 2 x 2, which is 2^4. 36 can be broken down into 2 x 2 x 3 x 3, which is 2^2 x 3^2.

 

Step 2: Now we found out the prime factors of 16 and 36. Since both numbers are perfect squares, we can find the square root easily. √(16/36) = √(2^4 / 2^2 x 3^2) = √(2^2 / 3^2) = 2/3, as both the numerator and denominator can be paired perfectly.

Professor Greenline from BrightChamps

Square Root of 16/36 by Long Division Method

The long division method is typically used for non-perfect square numbers, but it can also be applied to perfect square fractions for verification. Here’s how you can find the square root of 16/36 using the long division method:

 

Step 1: Divide 16 by 36, which simplifies to 0.4444...

 

Step 2: Find the square root of 0.4444... using long division:

 

Step 3: Group the numbers from right to left in pairs, here we start with 0.44.

 

Step 4: Find a number whose square is less than or equal to 44. In this case, 6^2 = 36.

 

Step 5: Subtract 36 from 44, giving a remainder of 8. Bring down two zeroes, making it 800.

 

Step 6: Doubling the result 6, we get 12. Find the next digit in the result, making it 12x, where x is chosen to fit 800.

 

Step 7: Continue the process to get the decimal approximation, which will eventually lead you to 0.6666...

Professor Greenline from BrightChamps

Square Root of 16/36 by Approximation Method

Approximation method is another technique for finding square roots, particularly useful for verifying results. Here is how we approximate the square root of 16/36:

 

Step 1: Recognize that 16/36 simplifies to 4/9, which are both perfect squares.

 

Step 2: Calculate the square roots: √16 = 4 and √36 = 6.

 

Step 3: Therefore, the square root of 16/36 is 4/6, which simplifies to 2/3. Thus, √(16/36) = 2/3, confirming the exact value.

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Common Mistakes and How to Avoid Them in the Square Root of 16/36

Students often make mistakes while finding the square root, such as forgetting about the negative square root or not simplifying fractions properly. 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 remind students that a number can have both positive and negative square roots. However, we usually consider only the positive square root for practical applications, unless specified otherwise.

 

For example, √(16/36) = 2/3, but there is also -2/3.

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Square Root of 16/36 Examples

Ray, the Character from BrightChamps Explaining Math Concepts
Max, the Girl Character from BrightChamps

Problem 1

Can you help Max find the area of a square box if its side length is given as √(25/49)?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

The area of the square is 25/49 square units.

Explanation

The area of the square = side^2.

The side length is given as √(25/49).

Area of the square = side^2 = (√(25/49))^2 = 25/49.

Therefore, the area of the square box is 25/49 square units.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 2

A square-shaped building measuring 16/36 square feet is built; if each of the sides is √(16/36), what will be the square feet of half of the building?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

8/36 square feet

Explanation

We can just divide the given area by 2 as the building is square-shaped.

Dividing 16/36 by 2 = 8/36.

So half of the building measures 8/36 square feet.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 3

Calculate √(16/36) x 5.

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

10/3

Explanation

The first step is to find the square root of 16/36, which is 2/3.

The second step is to multiply 2/3 by 5.

So (2/3) x 5 = 10/3.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (9/16 + 1/4)?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

The square root is 3/4

Explanation

To find the square root, we need to find the sum of (9/16 + 1/4).

Convert 1/4 to 4/16 to have a common denominator: 9/16 + 4/16 = 13/16.

Therefore, the square root of (13/16) is approximately ±3/4 when considering the closest simple fraction.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of a rectangle if its length 'l' is √(16/36) units and the width 'w' is 3 units.

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

We find the perimeter of the rectangle as 14/3 units.

Explanation

Perimeter of the rectangle = 2 × (length + width).

Perimeter = 2 × (√(16/36) + 3) = 2 × (2/3 + 3) = 2 × (11/3) = 22/3 units.

Max from BrightChamps Praising Clear Math Explanations
Ray Thinking Deeply About Math Problems

FAQ on Square Root of 16/36

1.What is √(16/36) in its simplest form?

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2.Mention the factors of 16 and 36.

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3.Calculate the product of 16 and 36.

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4.Are 16 and 36 prime numbers?

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5.What is the simplest form of 16/36?

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Professor Greenline from BrightChamps

Important Glossaries for the Square Root of 16/36

  • Square root: A square root is the inverse of a square. For 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, where p and q are integers and q ≠ 0.

 

  • Perfect square: A perfect square is an integer that is the square of an integer. For example, 16 is a perfect square because it equals 4^2.

 

  • Prime factorization: The process of expressing a number as a product of its prime factors. For example, the prime factorization of 36 is 2^2 x 3^2.

 

  • Fraction: A fraction represents a part of a whole or any number of equal parts. It is represented as p/q, where p is the numerator and q is the denominator.
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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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