114 LearnersLast updated on May 26th, 2025
Square Root of 36/16
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 fields like vehicle design, finance, etc. Here, we will discuss the square root of 36/16.
What is the Square Root of 36/16?
The square root is the inverse of the square of a number. 36/16 can be simplified to 9/4, which is a perfect square. The square root of 36/16 is expressed in both radical and exponential forms. In the radical form, it is expressed as √(36/16), whereas (36/16)^(1/2) in the exponential form. √(36/16) = 3/2 or 1.5, 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 36/16
The prime factorization method is used for perfect square numbers. Since 36/16 simplifies to a perfect square, we can use the prime factorization method directly. Let us now learn the following methods to verify the result:
- Prime factorization method
- Simplification method
Square Root of 36/16 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 36/16 is broken down into its prime factors.
Step 1: Simplify 36/16 to 9/4.
Step 2: Find the prime factors of 9 and 4: 9 = 3 x 3 4 = 2 x 2
Step 3: Now, take the square root of both the numerator and the denominator: √(9/4) = √9 / √4 = 3/2.
Thus, the square root of 36/16 is 3/2.
Square Root of 36/16 by Simplification Method
The simplification method involves simplifying the fraction first and then finding the square root. Let us now learn how to find the square root using the simplification method, step by step.
Step 1: Simplify the fraction 36/16 to 9/4.
Step 2: Calculate the square root of the simplified fraction: √(9/4) = √9 / √4 = 3/2.
So, the square root of 36/16 is 3/2 or 1.5.
Square Root of 36/16 by Rationalization Method
The rationalization method is useful for expressing the square root in a simplified manner. Now let us learn how to find the square root of 36/16 using the rationalization method.
Step 1: Simplify the fraction 36/16 to 9/4.
Step 2: Since 9/4 is a perfect square, directly find the square root: √(9/4) = 3/2.
Thus, the square root of 36/16 is 3/2 or 1.5.
Common Mistakes and How to Avoid Them in the Square Root of 36/16
Students can make mistakes while finding the square root, such as not simplifying fractions first or confusing rational numbers with irrational ones. Now let's look at a few of those mistakes in detail.
Mistake 1
Not Simplifying the Fraction
It is essential to simplify the fraction before finding its square root.
For example, not simplifying 36/16 to 9/4 can lead to wrong results. Always simplify fractions first.
Mistake 2
Misinterpreting the Square Root of a Fraction
Students might mistakenly calculate the square root of the numerator and denominator separately without simplifying the fraction first. Ensure fractions are simplified before applying square roots.
Mistake 3
Confusing Rational and Irrational Numbers
Students might confuse rational numbers with irrational ones.
For example, √(9/4) = 3/2 is rational, while √2 is irrational. Understanding the difference is crucial.
Mistake 4
Ignoring Negative Solutions
While finding square roots, students might ignore that a square root can be both positive and negative. However, in most real-world scenarios, the positive root is used.
Mistake 5
Overlooking Simplification Before Calculating
Skipping simplification can result in incorrect solutions. Always ensure that the fraction is in its simplest form before calculating the square root.
Square Root of 36/16 Examples
Problem 1
Can you help Lisa find the area of a square if its side length is given as √(36/16)?
The area of the square is 2.25 square units.
Explanation
The area of the square = side².
The side length is given as √(36/16) = 3/2.
Area of the square = (3/2)² = 3/2 × 3/2 = 9/4 = 2.25.
Therefore, the area of the square is 2.25 square units.
Problem 2
A square-shaped garden measuring 36/16 square meters is built; if each of the sides is √(36/16), what will be the square meters of half of the garden?
1.125 square meters
Explanation
We can just divide the given area by 2 as the garden is square-shaped.
Dividing 36/16 by 2 = 9/8 = 1.125.
So half of the garden measures 1.125 square meters.
Problem 3
Calculate √(36/16) × 8.
12
Explanation
The first step is to find the square root of 36/16 which is 1.5, the second step is to multiply 1.5 with 8.
So 1.5 × 8 = 12.
Problem 4
What will be the square root of (36 + 16)?
The square root is 7.
Explanation
To find the square root, we need to find the sum of (36 + 16).
36 + 16 = 52, and then √52 ≈ 7.211.
Therefore, the square root of (36 + 16) is approximately ±7.211.
Problem 5
Find the perimeter of a rectangle if its length ‘l’ is √(36/16) units and the width ‘w’ is 4 units.
The perimeter of the rectangle is 11 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Length = √(36/16) = 1.5 units.
Perimeter = 2 × (1.5 + 4)
= 2 × 5.5
= 11 units.
FAQ on Square Root of 36/16
1.What is √(36/16) in its simplest form?
2.Mention the factors of 36/16.
3.Calculate the square of 36/16.
4.Is 36/16 a prime number?
5.36/16 is divisible by?
6.How does learning Algebra help students in Australia make better decisions in daily life?
7.How can cultural or local activities in Australia support learning Algebra topics such as Square Root of 36/16?
8.How do technology and digital tools in Australia support learning Algebra and Square Root of 36/16?
9.Does learning Algebra support future career opportunities for students in Australia?
Important Glossaries for the Square Root of 36/16
- Square root: A square root is the inverse of a square. Example: 4² = 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 q is not equal to zero and p and q are integers.
- Simplification: Simplification involves reducing a fraction to its simplest form, making calculations easier.
- Perfect square: A perfect square is a number that has an integer as its square root. For example, 9 is a perfect square because √9 = 3.
- Fraction: A fraction represents a part of a whole number, expressed as a numerator divided by a denominator, such as 3/4.
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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.
