document.write( "Question 244765: How would I simplify √ł√5
\n" ); document.write( "I don't get how to simplify square roots in side of another square root. \n" ); document.write( "

Algebra.Com's Answer #178960 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "Hint: Remember that $\"root%283%2Cx%29=%28x%29%5E%281%2F3%29%5E%22%22\"$ . In addition, $\"sqrt%28x%29=%28x%29%5E%281%2F2%29%5E%22%22\"$ . Use these two equations along with the identity $\"%28x%5Ey%29%5Ez=x%5E%28yz%29\"$ to simplify the problem. Let me know if this hint helps or not. If not, then repost or ask me.\r
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\n" ); document.write( "\n" ); document.write( " $\"root%283%2Csqrt%285%29%29\"$ Start with the given expression.\r
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\n" ); document.write( "\n" ); document.write( " $\"root%283%2C5%5E%281%2F2%29%5E%22%22%29\"$ Rewrite $\"sqrt%285%29\"$ as $\"5%5E%281%2F2%29%5E%22%22\"$ using the property $\"sqrt%28x%29=%28x%29%5E%281%2F2%29%5E%22%22\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"%285%5E%281%2F2%29%29%5E%281%2F3%29\"$ Convert $\"root%283%2C5%5E%281%2F2%29%5E%22%22%29\"$ to $\"%285%5E%281%2F2%29%29%5E%281%2F3%29\"$ using the property $\"root%283%2Cx%29=%28x%29%5E%281%2F3%29%5E%22%22\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"5%5E%28%281%2F2%29%2A%281%2F3%29%29%5E%22%22\"$ Multiply the exponents using the idea that $\"%28x%5Ey%29%5Ez=x%5E%28yz%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"5%5E%28%281%2A1%29%2F%282%2A3%29%29%5E%22%22\"$ Combine the fractions.\r
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\n" ); document.write( "\n" ); document.write( " $\"5%5E%281%2F6%29%5E%22%22\"$ Multiply\r
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\n" ); document.write( "\n" ); document.write( " $\"root%286%2C5%29\"$ Convert back to radical notation\r
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\n" ); document.write( "\n" ); document.write( "So $\"root%283%2Csqrt%285%29%29=root%286%2C5%29\"$
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