document.write( "Question 201791: sqrt (56ab^3) / sqrt (7a) \n" ); document.write( "

Algebra.Com's Answer #152034 by Theo(13342) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"sqrt+%2856%2Aa%2Ab%5E3%29\"$ = $\"sqrt+%287%2Aa%2A8%2Ab%5E3%29\"$ = $\"sqrt%287%2Aa%29+%2A+sqrt+%288%2Ab%5E3%29\"$
\n" ); document.write( "your problem becomes:
\n" ); document.write( " $\"%28sqrt%287%2Aa%29+%2A+sqrt+%288%2Ab%5E3%29%29%2Fsqrt%287%2Aa%29\"$
\n" ); document.write( "which becomes
\n" ); document.write( " $\"sqrt%288%2Ab%5E3%29\"$
\n" ); document.write( "because $\"sqrt%287%2Aa%29\"$ cancels out (same in numerator and denominator).
\n" ); document.write( " $\"sqrt%288%2Ab%5E3%29\"$ can be reduced further (taking most out from under square root sign that you can) because 8 is a product of $\"2%5E2%2A2\"$ and $\"b%5E3\"$ is a product of $\"b%5E2%2Ab\"$ .
\n" ); document.write( " $\"sqrt%282%5E2%29\"$ is 2 and $\"sqrt%28b%5E2%29\"$ is b, so the final reduced answer is
\n" ); document.write( " $\"2%2Ab%2Asqrt%282%2Ab%29\"$
\n" ); document.write( "to prove your answer is correct, solve it both ways (with the original equation and the reduced equation).
\n" ); document.write( "let a = 10
\n" ); document.write( "let b = 20
\n" ); document.write( "with the reduced equation $\"2%2Ab%2Asqrt%282%2Ab%29\"$ = 252.9822128
\n" ); document.write( "with the original equation $\"sqrt%2856%2Aa%2Ab%5E3%29%2Fsqrt%287%2Aa%29\"$ = 252.9822128
\n" ); document.write( "since the answers are the same, the reduction is correct.
\n" ); document.write( "you can try some other numbers for a and b to prove it to yourself.
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