Question

Using prime factorization, find the square roots of

a) 11025
b) 4761

Answer 1

a) We have, 11025
$\begin{array}{cc}3& 11025\\ 3& 3675\\ 5& 1225\\ 5& 245\\ 7& 49\\ 7& 7\\ & 1\end{array}$
...(1 mark)
Now, $11025=\underset{–}{3\times 3}\times \underset{–}{5\times 5}\times \underset{–}{7\times 7}$
$\therefore$ Square root of $11025=\sqrt{11025}=3\times 5\times 7=105$...(1 mark)

b) We have, 4761
$\begin{array}{cc}3& 4761\\ 3& 1587\\ 23& 529\\ 23& 23\\ & 1\end{array}$
...(1 mark)
Now, $4761=\underset{–}{3\times 3}\times \underset{–}{23\times 23}$
$\therefore$ Square root of 4761 $=\sqrt{4761}=3\times 23=69$...(1 mark)