# Math Help - Radical Expressions

1. ## Radical Expressions

Urgent! Please help me simplify these expressions. I have no idea. Please show how each term is simplified. thank you.

2. Originally Posted by reiward
Urgent! Please help me simplify these expressions. I have no idea. Please show how each term is simplified. thank you.

Hi reiward,

This is truly some industrial strength algebra. I got the first one down fairly simple, but couldn't manipulate the last term to very much. Maybe it's stated incorrectly or something.

$\sqrt[6]{32 \sqrt{4n^{12}}} - \frac{n\sqrt{4n^2+16n+16}}{n+2}+\frac{n-1}{\sqrt[3]{n}-1}$

$\sqrt[6]{32 \cdot 2n^6} - \frac{n\sqrt{(2n+4)^2}}{n+2}+\frac{n-1}{\sqrt[3]{n}-1}$

$\sqrt[6]{2^6 \cdot n^6} - \frac{n(2n+4)}{n+2}+\frac{n-1}{\sqrt[3]{n}-1}$

$2n - \frac{2n(n+2}{n+2}+\frac{n-1}{\sqrt[3]{n}-1}$

$2n - 2n +\frac{n-1}{\sqrt[3]{n}-1}$

$\frac{n-1}{\sqrt[3]{n}-1}$

I messed around with this last term a while, but could never get it to anything simpler than it already is.

Now, for the second one.

$\frac{\sqrt{z^6}\cdot \sqrt[5]{2x^3y^2}}{\sqrt[4]{4x^2y^4z^8}} \div \frac{\sqrt[5]{64x^8y^{-3}}}{\sqrt[6]{8x^3}}$

$\frac{z^3 \cdot 2^{\frac{1}{5}}x^{\frac{3}{5}}y^{\frac{2}{5}}}{2^{ \frac{1}{2}}x^{\frac{1}{2}}yz^2}\cdot \frac{2^{\frac{1}{2}}x^{\frac{1}{2}}y^{\frac{3}{5} }}{2\cdot 2^{\frac{1}{5}}x\cdot x^{\frac{3}{5}}}=\frac{zy}{2xy}=\frac{z}{2x}$

3. ## thanks!

thank you! maybe thats the final answer for number 1. oh well, thank you very much

4. hi, we discussed the answers already, just wanna share. for the last term this is what we did.

$\frac{n-1}{\sqrt[3]{n}-1} * \frac{\sqrt[3]{n}^2 + \sqrt[3]{n} + 1}{\sqrt[3]{n}^2 + \sqrt[3]{n} + 1}$

then

$\frac{n-1} {n-1} \sqrt[3]{n}^2 + \sqrt[3]{n} + 1
$

so the answer is.

$\sqrt[3]{n}^2 + \sqrt[3]{n} + 1
$