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Math Help - Simplified Radical Form.

  1. #1
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    Simplified Radical Form.

    Can anyone help with this problem?




    Algebra is not my cup of tea.
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  2. #2
    Super Member

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    Hello, eraser851!

    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 . . .

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  3. #3
    Newbie DavePercy's Avatar
    Joined
    Feb 2008
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    You can distribute the radical over multiplication:

    <br />
\begin{array}{rcl}<br /> <br />
\sqrt[4]{96t^{12}u^7}<br />
&=&<br />
\sqrt[4]{96}\cdot\sqrt[4]{t^{12}}\cdot\sqrt[4]{u^7} \\<br /> <br />
&=&<br />
\sqrt[4]{16}<br />
\cdot\sqrt[4]{6}<br />
\cdot\sqrt[4]{t^{12}}<br />
\cdot\sqrt[4]{u^4}<br />
\cdot\sqrt[4]{u^3}<br />
\\<br />
&=&<br />
2<br />
\cdot\sqrt[4]{6}<br />
\cdot t^3<br />
\cdot u<br />
\cdot\sqrt[4]{u^3}<br />
\\&=&<br /> <br />
2t^3\sqrt[4]{6u^3}<br /> <br />
\end{array}<br />
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