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 9216.
The square root is the inverse of the square of the number. 9216 is a perfect square. The square root of 9216 is expressed in both radical and exponential forms. In radical form, it is expressed as √9216, whereas (9216)^(1/2) in exponential form. √9216 = 96, 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 can be used for perfect square numbers like 9216. When a number is a perfect square, the prime factorization method helps identify its square root. 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 9216 is broken down into its prime factors.
Step 1: Finding the prime factors of 9216
Breaking it down, we get 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 = 2^6 × 3^4
Step 2: Pair the prime factors. Since 9216 is a perfect square, we can pair all the prime factors.
Step 3: Multiply the factors in one group from each pair: (2^3 × 3^2 = 8 × 9 = 72). Since 9216 is a perfect square, the square root of 9216 is 96.
The long division method is particularly useful for both perfect and non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the square root using the long division method, step by step.
Step 1: To begin with, we need to group the numbers from right to left in pairs. For 9216, it is grouped as 92 and 16.
Step 2: Now we need to find a number whose square is less than or equal to the leftmost group, 92. We choose 9 since 9 × 9 = 81 ≤ 92. The quotient is 9, and the remainder is 11 after subtracting 81 from 92.
Step 3: Bring down the next pair, 16, to make the new dividend 1116. Add the old divisor with the same number 9 + 9, we get 18 which will be our new divisor.
Step 4: The new divisor will be 18n. We need to find n such that 18n × n ≤ 1116. Let n = 6, then 186 × 6 = 1116.
Step 5: Subtract 1116 from 1116; the remainder is 0.
The quotient is 96. Since the remainder is 0, the square root of 9216 is 96.
The approximation method is another way to find the square roots, and it is an easy method to find the square root of a given number. Since 9216 is a perfect square, the approximation method confirms the result but is not typically necessary for perfect squares.
Step 1: Identify the closest perfect square numbers around 9216. In this case, 9216 is itself a perfect square.
Step 2: Since we already found that √9216 is 96 using other methods, the approximation is not needed for this perfect square.
Thus, the square root of 9216 is 96.
Students often make mistakes while finding the square root, such as forgetting about the negative square root or skipping the long division method. Here are a few common mistakes students make, explained in detail.
Can you help Max find the area of a square box if its side length is given as √9216?
The area of the square is 9216 square units.
The area of a square = side².
The side length is given as √9216.
Area of the square = side² = √9216 × √9216 = 96 × 96 = 9216
Therefore, the area of the square box is 9216 square units.
A square-shaped building measuring 9216 square feet is built; if each of the sides is √9216, what will be the square feet of half of the building?
4608 square feet.
We can divide the given area by 2 as the building is square-shaped.
Dividing 9216 by 2 gives us 4608.
So half of the building measures 4608 square feet.
Calculate √9216 × 5.
480.
First, find the square root of 9216, which is 96.
Then multiply 96 by 5.
So, 96 × 5 = 480.
What will be the square root of (9216 + 64)?
The square root is 98.
To find the square root, first find the sum of (9216 + 64). 9216 + 64 = 9280, and then find √9280 ≈ 96.33.
Therefore, the square root of (9216 + 64) is approximately 98.
Find the perimeter of the rectangle if its length ‘l’ is √9216 units and the width ‘w’ is 50 units.
The perimeter of the rectangle is 292 units.
Perimeter of the rectangle = 2 × (length + width)
Perimeter = 2 × (√9216 + 50) = 2 × (96 + 50) = 2 × 146 = 292 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.