103 LearnersLast updated on May 26th, 2025
Square Root of 16/9
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 fields of vehicle design, finance, etc. Here, we will discuss the square root of 16/9.
What is the Square Root of 16/9?
The square root is the inverse of the square of the number. 16/9 is a perfect square. The square root of 16/9 is expressed in both radical and fractional form. In the radical form, it is expressed as, √(16/9), whereas in fractional form, it can be simplified to (4/3). The square root of 16/9 is 4/3, 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 16/9
The prime factorization method can be used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where the long-division method and approximation method are used. Let us now learn the following methods:
- Prime factorization method
- Long division method
- Approximation method
Square Root of 16/9 by Prime Factorization Method
The product of prime factors is the prime factorization of a number. Now let us look at how 16/9 is broken down into its prime factors.
Step 1: Finding the prime factors of 16 and 9 Breaking it down, we get 16 = 2 × 2 × 2 × 2 and 9 = 3 × 3.
Step 2: Now we found out the prime factors of 16 and 9. We pair the prime factors: (2 × 2) and (3).
Step 3: Since both 16 and 9 are perfect squares, we can find their square roots easily: √16 = 4 and √9 = 3.
Therefore, the square root of 16/9 using prime factorization is 4/3.
Square Root of 16/9 by Long Division Method
The long division method is particularly used for non-perfect square numbers. However, 16/9 is a perfect square, so the long division method is not necessary here. We can directly find the square root by simplifying the fraction to 4/3.
Square Root of 16/9 by Approximation Method
The approximation method is another method for finding the square roots. It is an easy method to find the square root of a given number. However, since 16/9 is a perfect square, approximation is not needed. The exact square root is 4/3.
Common Mistakes and How to Avoid Them in the Square Root of 16/9
Students do make mistakes while finding the square root, such as forgetting about the negative square root. Skipping steps in the long division method, etc. Now 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 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, √(16/9) = 4/3, but there is also -4/3 which should not be forgotten.
Square Root of 16/9 Examples
Problem 1
Can you help Max find the area of a square box if its side length is given as √(25/16)?
The area of the square is 25/16 square units.
Explanation
The area of the square = side^2.
The side length is given as √(25/16).
Area of the square = side^2
= (5/4) × (5/4)
= 25/16.
Therefore, the area of the square box is 25/16 square units.
Problem 2
A square-shaped field measures 16/9 square meters; if each of the sides is √(16/9), what will be the square meters of half of the field?
8/9 square meters
Explanation
We can just divide the given area by 2 as the field is square-shaped. Dividing 16/9 by 2, we get 8/9. So half of the field measures 8/9 square meters.
Problem 3
Calculate √(16/9) × 5.
20/3
Explanation
The first step is to find the square root of 16/9, which is 4/3.
The second step is to multiply 4/3 by 5.
So (4/3) × 5 = 20/3.
Problem 4
What will be the square root of (25/9 + 4/9)?
The square root is 3/2.
Explanation
To find the square root, we need to find the sum of (25/9 + 4/9).
25/9 + 4/9 = 29/9, and then the square root of 29/9 is approximately 3/2.
Therefore, the square root of (25/9 + 4/9) is ±3/2.
Problem 5
Find the perimeter of the rectangle if its length ‘l’ is √(25/16) units and the width ‘w’ is 6 units.
We find the perimeter of the rectangle as 14.5 units.
Explanation
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (√(25/16) + 6)
= 2 × (5/4 + 6)
= 2 × (29/4)
= 14.5 units.
FAQ on Square Root of 16/9
1.What is √(16/9) in its simplest form?
2.Mention the factors of 16 and 9.
3.Calculate the square of 16/9.
4.Is 16/9 a prime number?
5.16/9 is divisible by?
Important Glossaries for the Square Root of 16/9
- Square root: A square root is the inverse of a square. Example: (4/3)^2 = 16/9 and the inverse of the square is the square root, that is √(16/9) = 4/3.
- 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.
- Principal square root: A number has both positive and negative square roots; however, it is always the positive square root that has more prominence due to its uses in the real world. That is the reason it is also known as the principal square root.
- Fraction: A fraction represents a part of a whole or, more generally, any number of equal parts. It consists of a numerator and a denominator.
- Perfect square: A perfect square is a number that is the square of an integer or a fraction. For example, 16/9 is a perfect square because its square root is 4/3.
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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.
