Adding and Multiplying Radicals

[KimmyDean]

Hello,

I have been working on a few problems and keep getting stuck!

Simplify and reduce to lowest terms.

\(\displaystyle (\2 sqrt{3}-1)\)\(\displaystyle (\3 sqrt{3}+4)\)

I get:

\(\displaystyle 6 sqrt{3}^2+\8 sqrt{3}-\3 sqrt{3}-4\) then I combine like radicals and get:

\(\displaystyle 6*3+\5 sqrt{3}-4\)
and end up with \(\displaystyle 14+\5 sqrt{3}\)

Is that correct?


Another one is
\(\displaystyle sqrt{8}+ sqrt{32}\)

I get \(\displaystyle 2 sqrt{2}+8 sqrt{4}\)
= \(\displaystyle 10sqrt{2}\)

That doesn't seem right to me!

 

[pka]

The first is correct.

But \(\displaystyle sqrt{32}=sqrt{2^5}=4sqrt{2}.\)

 

[KimmyDean]

Thank you

3\(\displaystyle sqrt {-8x^12}\) = \(\displaystyle (-2x{^4})\)

Right concepts?

I am supposed to simplify this one too.

1/(\(\displaystyle sqrt{t-5}) + 3/sqrt{t+5})\)

=\(\displaystyle 3+5t+sqrt{t+5}\)



\(\displaystyle sqrt{20m^3b}\)

simplified does it equal 2mb\(\displaystyle sqrt{5m}\)??