document.write( "Question 367254: What is the square root of (5mn)^5 \n" ); document.write( "

Algebra.Com's Answer #261936 by jsmallt9(3758) $\"\"$ $\"About$

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$\"sqrt%28%285mn%29%5E5%29\"$
\n" ); document.write( "To simplify any square root you look for perfect square factors. So we will factor the radicand (the expression inside the radical) into as many perfect square factors as possible:
\n" ); document.write( " $\"sqrt%285%5E5m%5E5n%5E5%29\"$
\n" ); document.write( " $\"sqrt%285%5E2%2A5%5E2%2A5%2Am%5E2%2Am%5E2%2Am%2An%5E2%2An%5E2%2An%29\"$
\n" ); document.write( "Using the Commutative property we can rearrange the factors. I like to put all the perfect square factors in front:
\n" ); document.write( " $\"sqrt%285%5E2%2A5%5E2%2Am%5E2%2Am%5E2%2An%5E2%2An%5E2%2A5%2Am%2An%29\"$
\n" ); document.write( "Next we can use the property of radicals, $\"root%28a%2C+p%2Aq%29+=+root%28a%2C+p%29+%2A+root%28a%2C+q%29\"$ to separate all the perfect square factors into separate square roots:
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\n" ); document.write( "Now we can simplify the square roots of the perfect squares:
\n" ); document.write( " $\"5%2A5%2Am%2Am%2An%2An%2Asqrt%285%2Am%2An%29\"$
\n" ); document.write( "which simplifies to:
\n" ); document.write( " $\"25m%5E2%2An%5E2%2Asqrt%285mn%29\"$ \n" ); document.write( "

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