127 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.
Mistake 2
Not adding square root symbol in proper places
Not using the square root properly is another mistake that children make. To resolve this, we need to teach children that simplifying the numbers inside the square root is important and then moving on to the next step.
For example, √(a/b + c/d) ≠ √(a/b) + √(c/d). The right way of using roots is √(a/b + c/d) = √(sum of the fractions).
Mistake 3
Not finding the correct value of a non-perfect square
The first step that needs to be taught to children is to simplify the numbers inside the square root when dealing with non-perfect squares. This is important so that students do not make mistakes while identifying the approximate value. For perfect squares like 16/9, direct calculation is possible.
Mistake 4
Confusing the square root symbol with the cube root
Students need to be taught the difference between cube root and square root constantly, as this will help them avoid mistakes.
For example, √(16/9) and ∛(16/9) are different.
Mistake 5
Making mistakes in long division
Finding a square root using the long division method involves many steps. Due to this, many students might skip a step accidentally, which results in a wrong answer. However, for perfect squares like 16/9, the long division method is not required.
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.
