Question

Find the square root of $9604$ by the Prime Factorisation Method.

Answer 1

Step 1: Determine the prime factors of the given number:

Given number: $9604$.

Factorize the given number.

$\begin{array}{cc}2& 9604\\ 2& 4802\\ 7& 2401\\ 7& 343\\ 7& 49\\ 7& 7\\ & 1\end{array}$

Thus, $9604=2\times 2\times 7\times 7\times 7\times 7$.

Step 2: Calculate the square root of the given number:

$$\begin{gathered} 9604=\left(2\times 2\right)\times \left(7\times 7\right)\times \left(7\times 7\right) \\ \Rightarrow 9604={\left(2\right)}^2\times {\left(7\right)}^2\times {\left(7\right)}^2 \\ \Rightarrow 9604={\left(2\times 7\times 7\right)}^2 \end{gathered}$$

Take square root on both sides of the equation.

$$\begin{gathered} \Rightarrow \sqrt{9604}=\sqrt{{\left(2\times 7\times 7\right)}^2} \\ \Rightarrow \sqrt{9604}=\left(2\times 7\times 7\right) \\ \Rightarrow \sqrt{9604}=98 \end{gathered}$$

Therefore, the square root of the $9604$ is $98$.