Question 1101935
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the difference between an integer and its square root is 6. find the integer.
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<pre>
Since the difference between an integer and its square root is 6, the square root itself is an integer.


Let x be the square root; then the integer under the question is x^2, and the condition says


x^2 - x = 6,   or  x*(x-1) = 6.


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.


There is only one such a divisor of 6: it is 3.  


Hence, the integer under the question is 9.
</pre>

Solved.