document.write( "Question 375846: if a and b are positive integers and (a^(1/2) * b^(1/3)) = 432, what is the value of ab? \n" ); document.write( "

Algebra.Com's Answer #267293 by Fombitz(32388) $\"\"$ $\"About$

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$\"a%5E%281%2F2%29%2A+b%5E%281%2F3%29+=+432\"$
\n" ); document.write( "Square both sides.
\n" ); document.write( " $\"a%5E%283%2F2%29%2Ab=432%5E3\"$
\n" ); document.write( "Cube both sides.
\n" ); document.write( " $\"a%5E3b%5E2=432%5E6\"$
\n" ); document.write( "Look at factors of 432,
\n" ); document.write( " $\"a%5E3b%5E2=%282%5E4%2A3%5E3%29%5E6\"$
\n" ); document.write( " $\"a%5E3b%5E2=2%5E24%2A3%5E18\"$
\n" ); document.write( "Two solutions:
\n" ); document.write( " $\"a%5E3=2%5E24\"$ , $\"highlight%28+a=2%5E8%29\"$
\n" ); document.write( " $\"b%5E2=3%5E18\"$ , $\"highlight%28b=3%5E9%29\"$
\n" ); document.write( "or
\n" ); document.write( " $\"a%5E3=3%5E18\"$ , $\"highlight_green%28a=3%5E6%29\"$
\n" ); document.write( " $\"b%5E2=2%5E24\"$ , $\"highlight_green%28b=2%5E12%29\"$
\n" ); document.write( " \n" ); document.write( "

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