123 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?
6.How does learning Algebra help students in Qatar make better decisions in daily life?
7.How can cultural or local activities in Qatar support learning Algebra topics such as Square Root of 16/36?
8.How do technology and digital tools in Qatar support learning Algebra and Square Root of 16/36?
9.Does learning Algebra support future career opportunities for students in Qatar?
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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