Question

Evaluate: $\sqrt{98}\times \sqrt{162}$

Answer 1

Lets do prime factorisation for $98$ and $162$

$\begin{array}{cc}2& 98\\ 7& 49\\ 7& 7\\ & 1\end{array}$

$\begin{array}{cc}2& 162\\ 3& 81\\ 3& 27\\ 3& 9\\ 3& 3\\ & 1\end{array}$

Now,

$\sqrt{98}\times \sqrt{162}=\sqrt{98\times 162}$
$=\sqrt{2\times 7\times 7\times 2\times 3\times 3\times 3\times 3}$
$=\sqrt{\overline{2\times 2}\times \overline{7\times 7}\times \overline{3\times 3}\times \overline{3\times 3}}$
$=2\times 7\times 3\times 3$
$=126$

$\therefore \sqrt{98}\times \sqrt{162}=\sqrt{98\times 162}=126$