# 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,

$2\times2\times2\times\sqrt[2]{15}$

• The $16\times 8$ inside the square root is $(8)(8)(2)$. So we want $\sqrt[2]{(8)(8)(2)(5)(3)}$. Commented Sep 23, 2014 at 4:23
• Can we write it as $\sqrt[2]{2*2*2*2*2*2*5*3}$ Commented Sep 23, 2014 at 4:25
• Your count is wrong. There are $7$ (seven) $2$'s. Commented Sep 23, 2014 at 4:26

$16 = 2^4$

$8 = 2^3$

$\sqrt{(16)(8)(5)(3)} = \sqrt{(2^4)(2^3)(5)(3)} = \sqrt{(2^{3+4})(5)(3)} = \sqrt{(2^6)(2)(5)(3)}$

$= \sqrt{(8^2)(2)(5)(3)} = 8\sqrt{(2)(5)(3)} = 8 \sqrt{30}$

You honestly just took out an extra two. Happens to the best of us. :)

• Thank you! Got the answer! Commented Sep 23, 2014 at 4:43

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}

• Oh yeah! Silly mistake of mine. Thanks for the help though. Commented Sep 23, 2014 at 4:26