127 LearnersLast updated on May 26th, 2025
Square Root of 16/36
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.
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.
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
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.
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...
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.
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
Forgetting about the negative square root
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.
Mistake 2
Not simplifying fractions before finding the square root
One common mistake is not simplifying a fraction to its lowest terms before attempting to find the square root.
For example, not simplifying 16/36 to 4/9 can lead to unnecessary complications.
Mistake 3
Confusing the square root symbol with the cube root
Students need to distinguish between the square root and cube root symbols to avoid confusion.
For example, √(16/36) and ∛(16/36) are different operations with different results.
Mistake 4
Incorrect use of the square root symbol
Another mistake is incorrect usage of the square root symbol, such as assuming √(a + b) = √a + √b, which is incorrect. The correct approach is to find the sum first and then take the square root.
Mistake 5
Making mistakes in long division
Calculating a square root using the long division method involves many steps, and students can accidentally skip steps or perform incorrect calculations. This may lead to incorrect results.
Square Root of 16/36 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √(25/49)?
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.
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?
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.
Problem 3
Calculate √(16/36) x 5.
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.
Problem 4
What will be the square root of (9/16 + 1/4)?
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.
Problem 5
Find the perimeter of a rectangle if its length 'l' is √(16/36) units and the width 'w' is 3 units.
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.
FAQ on Square Root of 16/36
1.What is √(16/36) in its simplest form?
2.Mention the factors of 16 and 36.
3.Calculate the product of 16 and 36.
4.Are 16 and 36 prime numbers?
5.What is the simplest form of 16/36?
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.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
