Question

Find the square root of 9216.

Answer 1

Hint: To solve this question we will first of all define what is a square root then we will proceed to find the square root of the given number. The number which is given as 9216.

Complete step by step answer:
A square root is a number which produces a specified quantity when multiplied by itself.
We have to find the square root of 9216. We will use the definition of square root and apply it on 9216 to get the desired result.
We will factorise the given number using the prime factorisation.
The prime factorisation of the number 9216 is given by,
\[9216=(2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2)(3\times \text{3)}\]
\[\Rightarrow 9216=1024(9)\]
Taking square root on both the sides of the equation we get,
\[\Rightarrow \sqrt{9216}=\sqrt{1024(9)}\]
Removing the square root from the right-side of the above equation,
\[9216=(2\times 2\times 2\times 2\times 2)(3)\]
\[\Rightarrow \sqrt{9216}=96\]

Therefore, we get the square root of the given number 9216 as 96, which is the required solution.

Note: The possibility of error in the above given question can be at the point where you can take two numbers common as one together and leave one of the numbers obtained in prime factorisation aside which would be wrong and hence will give the wrong solution. Therefore, always go for expanding the given term by factorisation and then make two terms common as one.