document.write( "Question 195063: simplilfy: √[144x^10y^12z^18] \n" ); document.write( "

Algebra.Com's Answer #146362 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( " $\"sqrt%28144%2Ax%5E10%2Ay%5E12%2Az%5E18%29\"$ Start with the given expression.\r
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\n" ); document.write( "\n" ); document.write( " $\"sqrt%28144%2Ax%5E2%2Ax%5E2%2Ax%5E2%2Ax%5E2%2Ax%5E2%2Ay%5E12%2Az%5E18%29\"$ Factor $\"x%5E10\"$ into $\"x%5E2%2Ax%5E2%2Ax%5E2%2Ax%5E2%2Ax%5E2\"$ \r
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Factor $\"y%5E12\"$ into $\"y%5E2%2Ay%5E2%2Ay%5E2%2Ay%5E2%2Ay%5E2%2Ay%5E2\"$ \r
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Factor $\"z%5E18\"$ into $\"z%5E2%2Az%5E2%2Az%5E2%2Az%5E2%2Az%5E2%2Az%5E2%2Az%5E2%2Az%5E2%2Az%5E2\"$ \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 $\"144\"$ to get $\"12\"$ .\r
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Take the square root of $\"x%5E2\"$ to get $\"x\"$ .\r
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Take the square root of $\"y%5E2\"$ to get $\"y\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"12%2Ax%2Ax%2Ax%2Ax%2Ax%2Ay%2Ay%2Ay%2Ay%2Ay%2Ay%2Az%2Az%2Az%2Az%2Az%2Az%2Az%2Az%2Az\"$ Take the square root of $\"z%5E2\"$ to get $\"z\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"12x%5E5y%5E6z%5E9\"$ 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 $\"sqrt%28144%2Ax%5E10%2Ay%5E12%2Az%5E18%29\"$ simplifies to $\"12x%5E5y%5E6z%5E9\"$ \r
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\n" ); document.write( "\n" ); document.write( "In other words, $\"sqrt%28144%2Ax%5E10%2Ay%5E12%2Az%5E18%29=12x%5E5y%5E6z%5E9\"$ where every variable is non-negative.
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