# Simplified Radical Form.

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• March 7th 2008, 12:07 PM
eraser851
Simplified Radical Form.
Can anyone help with this problem?

http://img.photobucket.com/albums/v2...adicalform.jpg

Algebra is not my cup of tea.
• March 7th 2008, 12:34 PM
Soroban
Hello, eraser851!

Quote:

Simplify: . $\sqrt[4]{96t^{12}u^7}$

We have: . $\sqrt[4]{96\cdot t^{12}\cdot y^7} \;= \;\sqrt[4]{16\cdot6\cdot t^{12}\cdot u^4\cdot u^3} \;=\;\sqrt[4]{16}\cdot\sqrt[4]{6}\cdot\sqrt[4]{t^{12}}\cdot\sqrt[4]{u^4}\cdot\sqrt[4]{u^3}$

. . . $= \;2\cdot\sqrt[4]{6}\cdot t^3\cdot u\cdot\sqrt[4]{u^3} \;=\;2t^3u\!\cdot\!\sqrt[4]{6u^3}$

Hope you followed all that . . .

• March 7th 2008, 01:16 PM
DavePercy
You can distribute the radical over multiplication:

$
\begin{array}{rcl}

\sqrt[4]{96t^{12}u^7}
&=&
\sqrt[4]{96}\cdot\sqrt[4]{t^{12}}\cdot\sqrt[4]{u^7} \\

&=&
\sqrt[4]{16}
\cdot\sqrt[4]{6}
\cdot\sqrt[4]{t^{12}}
\cdot\sqrt[4]{u^4}
\cdot\sqrt[4]{u^3}
\\
&=&
2
\cdot\sqrt[4]{6}
\cdot t^3
\cdot u
\cdot\sqrt[4]{u^3}
\\&=&

2t^3\sqrt[4]{6u^3}

\end{array}
$