Last updated on May 26th, 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.
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.
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:
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.
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.
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.
Can you help Max find the area of a square box if its side length is given as √(81/16)?
The area of the square is 5.0625 square units.
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.
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?
2.53125 square feet
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.
Calculate √(81/16) × 5.
11.25
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.
What will be the square root of (81 + 16)?
The square root is 9.89
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.
Find the perimeter of the rectangle if its length ‘l’ is √(81/16) units and the width ‘w’ is 38 units.
We find the perimeter of the rectangle as 96.5 units.
Perimeter of the rectangle = 2 × (length + width).
Perimeter = 2 × (9/4 + 38) = 2 × (2.25 + 38) = 2 × 40.25 = 80.5 units.
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.
: He loves to play the quiz with kids through algebra to make kids love it.