document.write( "Question 1195200: Find the least integer by which 8100 must be multiplied to obtain a perfect cube \n" ); document.write( "

Algebra.Com's Answer #827611 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "Find the least integer by which 8100 must be multiplied to obtain a perfect cube
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document.write( "8100 = 81*100 = 9^2*10^2 = 2^2*3^4*5^2.\r\n" );
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document.write( "To make a perfect cube, we should have indexes at prime factors multiple of 3.\r\n" );
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document.write( "From here, it is clear that the least such integer number to multiply is  2*3^2*5 = 9*10 = 90.\r\n" );
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document.write( "Then the product is  8100*90 = 729000.\r\n" );
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document.write( "CHECK.   = 90.\r\n" );
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document.write( "ANSWER.  The least integer by which 8100 must be multiplied to obtain a perfect cube is 90.\r\n" );
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