Question

Find the square root of 1296 by prime factorisation.

• A. 34
• B. 36
• C. 26
• D. 64

Answer 1

The correct option is B 36

The given number is 1296. Lets do prime factorisation,

\begin{tabular}{c|c} 3 & 1296 \\ \hline 3 & 432 \\ \hline 3 & 144 \\ \hline 3 & 48 \\ \hline 2 & 16 \\ \hline 2 & 8 \\ \hline 2 & 4 \\ \hline 2 & 2 \\ \hline & 1 \end{tabular}
So we get $1296=3\times 3\times 3\times 3\times 2\times 2\times 2\times 2=3^4\times 2^4$
$\sqrt{1296}=\sqrt{3^4\times 2^4}=3^2\times 2^2$