document.write( "Question 1101935: the difference between an integer and its square root is 6. find the integer. \n" ); document.write( "

Algebra.Com's Answer #716586 by ikleyn(52787) $\"\"$ $\"About$

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\n" ); document.write( "the difference between an integer and its square root is 6. find the integer.
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document.write( "Since the difference between an integer and its square root is 6, the square root itself is an integer.\r\n" );
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document.write( "Let x be the square root; then the integer under the question is x^2, and the condition says\r\n" );
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document.write( "x^2 - x = 6,   or  x*(x-1) = 6.\r\n" );
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document.write( "Hence, x is the divisor of 6, such that (x-1) is the divisor of 6 too; and the product of these two consecutive integers is 6.\r\n" );
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document.write( "There is only one such a divisor of 6: it is 3.  \r\n" );
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document.write( "Hence, the integer under the question is 9.\r\n" );
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