document.write( "Question 1049891: If z = 2¹⁴∙3²⁰, what is the largest
\n" ); document.write( "power of 12 that evenly divides into the square root of z? \n" ); document.write( "

Algebra.Com's Answer #665458 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!
The solution above is incorrect!
\n" ); document.write( "

\r\n" );
document.write( "If z = 2¹⁴∙3²⁰, what is the largest \r\n" );
document.write( "power of 12 that evenly divides into the square root of z?\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Let p = the largest power of 12 that evenly divides into the\r\n" );
document.write( "square root of z\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "We are given:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "We find the square root of z\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now we divide  INTO , which amounts to\r\n" );
document.write( "dividing  BY \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Subtracting exponents on the right\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Negative exponents cause denominators. Therefore both those \r\n" );
document.write( "exponents must be non-negative (greater than or equal to zero) \r\n" );
document.write( "in order for the above result to be an integer, so we have:\r\n" );
document.write( "\r\n" );
document.write( " and \r\n" );
document.write( "\r\n" );
document.write( " and \r\n" );
document.write( "\r\n" );
document.write( "Remember that the inequality reverses when dividing \r\n" );
document.write( "by a negative number:\r\n" );
document.write( "\r\n" );
document.write( " and \r\n" );
document.write( "\r\n" );
document.write( "  and \r\n" );
document.write( "\r\n" );
document.write( " and \r\n" );
document.write( "\r\n" );
document.write( "The largest integer value of p that satisfies both those is p = 3.\r\n" );
document.write( "\r\n" );
document.write( "Answer: The largest power of 12 that evenly divides into the square \r\n" );
document.write( "root of z is 3.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\r
\n" );
document.write( "\n" );
document.write( " \n" );
document.write( "

\n" );