Square Root of 16/9
2026-02-28 06:15 Diff
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Last updated on August 5, 2025

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.

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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.

Problem 1

Can you help Max find the area of a square box if its side length is given as √(25/16)?

Okay, lets begin

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.

Well explained 👍

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?

Okay, lets begin

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.

Well explained 👍

Problem 3

Calculate √(16/9) × 5.

Okay, lets begin

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.

Well explained 👍

Problem 4

What will be the square root of (25/9 + 4/9)?

Okay, lets begin

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.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √(25/16) units and the width ‘w’ is 6 units.

Okay, lets begin

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.

Well explained 👍

FAQ on Square Root of 16/9

1.What is √(16/9) in its simplest form?

The prime factorization of 16 is 2 × 2 × 2 × 2 and 9 is 3 × 3, so the simplest form of √(16/9) is 4/3.

2.Mention the factors of 16 and 9.

Factors of 16 are 1, 2, 4, 8, and 16, while factors of 9 are 1, 3, and 9.

3.Calculate the square of 16/9.

We get the square of 16/9 by multiplying the number by itself, that is (16/9) × (16/9) = 256/81.

4.Is 16/9 a prime number?

5.16/9 is divisible by?

16 and 9 have their own factors, but as a fraction, 16/9 is not divisible by any whole number except for 1.

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.