Find the square root of the 9216 by the prime factorisation method.

A. 96

B. 86

C. 106

D. 76

To find the square root of 9216 using the prime factorization method, we first need to break down the number into its prime factors. This method involves expressing the number as a product of prime numbers, which can then help us easily find the square root.

Step 1: Prime Factorization of 9216

We start by dividing 9216 by the smallest prime number, which is 2, and continue dividing until we can no longer divide evenly.

• 9216 ÷ 2 = 4608
• 4608 ÷ 2 = 2304
• 2304 ÷ 2 = 1152
• 1152 ÷ 2 = 576
• 576 ÷ 2 = 288
• 288 ÷ 2 = 144
• 144 ÷ 2 = 72
• 72 ÷ 2 = 36
• 36 ÷ 2 = 18
• 18 ÷ 2 = 9
• 9 ÷ 3 = 3
• 3 ÷ 3 = 1

Now, we can summarize the prime factorization of 9216:

9216 = 2^10 × 3^2

Step 2: Finding the Square Root

To find the square root, we take the square root of each prime factor raised to its respective power. The square root of a product is the product of the square roots.

• √(2^10) = 2^(10/2) = 2^5 = 32
• √(3^2) = 3^(2/2) = 3^1 = 3

Now, we multiply these results together to find the square root of 9216:

√9216 = 32 × 3 = 96

Final Result

The square root of 9216 is 96. Therefore, the correct answer is A. 96.