document.write( "Question 1152651: Hi\r
\n" ); document.write( "\n" ); document.write( "Find the smallest value of x such that 1125x is a perfect square.\r
\n" ); document.write( "\n" ); document.write( "Hence find the value of the square root of 1125x.\r
\n" ); document.write( "\n" ); document.write( "Thanks \n" ); document.write( "
Algebra.Com's Answer #774691 by rothauserc(4718)\"\" \"About 
You can put this solution on YOUR website!
Consider the factors of 1125, looking for the largest perfect square which is a factor
\n" ); document.write( ":
\n" ); document.write( "1,3,5,9,15,25,45,75,125,225,375,1125
\n" ); document.write( ":
\n" ); document.write( "We see that 225 * 5 = 1125, therefore
\n" ); document.write( ":
\n" ); document.write( "1125x = 5 * 225 * x
\n" ); document.write( ":
\n" ); document.write( "if x = 5, we know that 1125 * 5 = 5625 and square root(5625) = 75, therefore
\n" ); document.write( ":
\n" ); document.write( "75^2 = 5625 is a perfect square
\n" ); document.write( ":
\n" ); document.write( "We know that 1125 * 1 is not a perfect square so
\n" ); document.write( ":
\n" ); document.write( "I submit that x = 5 is the smallest whole number when multiplied by 1125 yields a perfect square
\n" ); document.write( ":
\n" ); document.write( "I will leave it to you to check 2, 3, 4
\n" ); document.write( ":
\n" ); document.write( " \n" ); document.write( "
\n" );