Question

Find the square root of $9216$ by the Prime Factorisation method.

Answer 1

Step 1: Determine the prime factors of the given number

Given number: $9216$.

Factorize the given number.

$\begin{array}{cc}2& 9216\\ 2& 4608\\ 2& 2304\\ 2& 1152\\ 2& 576\\ 2& 288\\ 2& 144\\ 2& 72\\ 2& 36\\ 2& 18\\ 3& 9\\ 3& 3\\ & 1\end{array}$

Thus, $9216=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 3\times 3$.

Step 2: Calculate the square root of the given number

$\begin{array}{rrcl}\Rightarrow & 9216& =& \left(2\times 2\right)\times \left(2\times 2\right)\times \left(2\times 2\right)\times \left(2\times 2\right)\times \left(2\times 2\right)\times \left(3\times 3\right)\\ \Rightarrow & 9216& =& {\left(2\right)}^2\times {\left(2\right)}^2\times {\left(2\right)}^2\times {\left(2\right)}^2\times {\left(2\right)}^2\times {\left(3\right)}^2\\ \Rightarrow & 9216& =& {\left(2\times 2\times 2\times 2\times 2\times 3\right)}^2\\ \Rightarrow & \sqrt{9216}& =& \sqrt{{\left(96\right)}^2}\\ \Rightarrow & \sqrt{9216}& =& 96\end{array}$

Therefore, the square root of the $9216$ is $96$.