<s>[INST] Clearing the confusion of the area In the example 1:
They are finding the area as $8$ $\sqrt[2]{30}$. But, I am finding $8$ $\sqrt[2]{15}$.
I have done $\sqrt[2]{16\times5\times8\times3}$
Then,
Breaking it up,
$2\times2\times2\times\sqrt[2]{15}$
Please help me clear my confusion.

 [/INST] I think you're just forgetting to multiply by two.
Note that 
$$
\begin{align}
\sqrt{16\cdot 5\cdot 8\cdot 3} &= \sqrt{4 \cdot 4 \cdot 5 \cdot 4 \cdot 2 \cdot 3}\\
&= \sqrt{4}\sqrt{4}\sqrt{4}\sqrt{5 \cdot 2 \cdot 3}\\
&= 2 \cdot 2 \cdot 2 \sqrt{5 \cdot 2 \cdot 3}\\
&= 8 \sqrt{5 \cdot 2 \cdot 3}\\
&= 8 \sqrt{30}\\
\end{align}
$$
</s>