document.write( "Question 253918: Simplify the radical expression: $\"+sqrt%28+125x%5E5y%5E2z%5E4%29+\"$
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Algebra.Com's Answer #186270 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( " $\"sqrt%28125%2Ax%5E5%2Ay%5E2%2Az%5E4%29\"$ Start with the given expression.\r
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\n" ); document.write( "\n" ); document.write( " $\"sqrt%2825%2A5%2Ax%5E5%2Ay%5E2%2Az%5E4%29\"$ Factor $\"125\"$ into $\"25%2A5\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"sqrt%2825%2A5%2Ax%5E2%2Ax%5E2%2Ax%2Ay%5E2%2Az%5E4%29\"$ Factor $\"x%5E5\"$ into $\"x%5E2%2Ax%5E2%2Ax\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"sqrt%2825%2A5%2Ax%5E2%2Ax%5E2%2Ax%2Ay%5E2%2Az%5E2%2Az%5E2%29\"$ Factor $\"z%5E4\"$ into $\"z%5E2%2Az%5E2\"$ \r
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Break up the square root using the identity $\"sqrt%28A%2AB%29=sqrt%28A%29%2Asqrt%28B%29\"$ .\r
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Take the square root of $\"25\"$ to get $\"5\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"5%2Asqrt%285%29%2Ax%2Ax%2Asqrt%28x%29%2Asqrt%28y%5E2%29%2Asqrt%28z%5E2%29%2Asqrt%28z%5E2%29\"$ Take the square root of $\"x%5E2\"$ to get $\"x\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"5%2Asqrt%285%29%2Ax%2Ax%2Asqrt%28x%29%2Ay%2Asqrt%28z%5E2%29%2Asqrt%28z%5E2%29\"$ Take the square root of $\"y%5E2\"$ to get $\"y\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"5%2Asqrt%285%29%2Ax%2Ax%2Asqrt%28x%29%2Ay%2Az%2Az\"$ Take the square root of $\"z%5E2\"$ to get $\"z\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"5x%5E2yz%5E2%2Asqrt%285x%29\"$ Rearrange and multiply the terms.\r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"sqrt%28125%2Ax%5E5%2Ay%5E2%2Az%5E4%29\"$ simplifies to $\"5x%5E2yz%5E2%2Asqrt%285x%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "In other words, $\"sqrt%28125%2Ax%5E5%2Ay%5E2%2Az%5E4%29=5x%5E2yz%5E2%2Asqrt%285x%29\"$ where every variable is non-negative.
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