Square Root of 81/16
2026-02-28 06:03 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-81/16

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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 fields like vehicle design, finance, etc. Here, we will discuss the square root of 81/16.

What is the Square Root of 81/16?

The square root is the inverse of the square of the number. 81/16 is a perfect square. The square root of 81/16 is expressed in both radical and exponential form. In the radical form, it is expressed as √(81/16), whereas (81/16)^(1/2) in the exponential form. √(81/16) = 9/4, 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 81/16

The prime factorization method is used for perfect square numbers. Since 81/16 is a perfect square, we can use the prime factorization method. Let us now learn the following methods:

  • Prime factorization method
  • Simplification method

Square Root of 81/16 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 81 and 16 are broken down into their prime factors.

Step 1: Finding the prime factors of 81 and 16.

81 is 3 × 3 × 3 × 3 (or 3^4) 16 is 2 × 2 × 2 × 2 (or 2^4)

Step 2: Now we found out the prime factors of 81 and 16. Since both are perfect squares, the square root of 81 is 3^2 = 9, and the square root of 16 is 2^2 = 4.

Therefore, √(81/16) = 9/4.

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Square Root of 81/16 by Simplification Method

The simplification method is another method for finding the square roots, it is an easy method to find the square root of a given number. Now let us learn how to find the square root of 81/16 using the simplification method.

Step 1: Simplify the numerator and the denominator separately. The numerator is 81, and the denominator is 16. The square roots of 81 and 16 are 9 and 4, respectively.

Step 2: Use the formula: √(a/b) = √a/√b.

Therefore, √(81/16) = √81/√16 = 9/4.

Common Mistakes and How to Avoid Them in the Square Root of 81/16

Students do make mistakes while finding the square root, like forgetting about the negative square root. Skipping simplification methods, 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 √(81/16)?

Okay, lets begin

The area of the square is 5.0625 square units.

Explanation

The area of the square = side^2.

The side length is given as √(81/16) = 9/4.

Area of the square = (9/4)^2 = 81/16 = 5.0625.

Therefore, the area of the square box is 5.0625 square units.

Well explained 👍

Problem 2

A square-shaped building measuring 81/16 square feet is built; if each of the sides is √(81/16), what will be the square feet of half of the building?

Okay, lets begin

2.53125 square feet

Explanation

We can just divide the given area by 2 as the building is square-shaped.

Dividing 81/16 by 2 = 81/32 = 2.53125.

So half of the building measures 2.53125 square feet.

Well explained 👍

Problem 3

Calculate √(81/16) × 5.

Okay, lets begin

11.25

Explanation

The first step is to find the square root of 81/16 which is 9/4.

The second step is to multiply 9/4 with 5.

So (9/4) × 5 = 45/4 = 11.25.

Well explained 👍

Problem 4

What will be the square root of (81 + 16)?

Okay, lets begin

The square root is 9.89

Explanation

To find the square root, we need to find the sum of (81 + 16). 81 + 16 = 97, and then √97 ≈ 9.849.

Therefore, the square root of (81 + 16) is approximately ±9.89.

Well explained 👍

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √(81/16) units and the width ‘w’ is 38 units.

Okay, lets begin

We find the perimeter of the rectangle as 96.5 units.

Explanation

Perimeter of the rectangle = 2 × (length + width).

Perimeter = 2 × (9/4 + 38) = 2 × (2.25 + 38) = 2 × 40.25 = 80.5 units.

Well explained 👍

FAQ on Square Root of 81/16

1.What is √(81/16) in its simplest form?

The prime factorization of 81 is 3 × 3 × 3 × 3, and 16 is 2 × 2 × 2 × 2, so the simplest form of √(81/16) = 9/4.

2.Mention the factors of 81 and 16.

Factors of 81 are 1, 3, 9, 27, and 81. Factors of 16 are 1, 2, 4, 8, and 16.

3.Calculate the square of 81/16.

We get the square of 81/16 by multiplying the number by itself, that is (81/16) × (81/16) = 6561/256.

4.Is 81/16 a rational number?

Yes, 81/16 is a rational number, as it can be expressed as a fraction where both the numerator and the denominator are integers.

5.81/16 is divisible by?

81/16 is a fraction, and its divisibility depends on the context. However, the numerator 81 is divisible by 1, 3, 9, 27, and 81, and the denominator 16 is divisible by 1, 2, 4, 8, and 16.

Important Glossaries for the Square Root of 81/16

  • Square root: A square root is the inverse of a square. 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 q is not equal to zero, and p and q are integers.
  • Perfect square: A perfect square is a number that is the square of an integer. For example, 16 is a perfect square because 4 × 4 = 16.
  • Fraction: A fraction is a numerical quantity that is not a whole number, represented by two numbers separated by a slash, such as 3/4.
  • Simplification: Simplification is the process of reducing a mathematical expression to its simplest form.

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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.