Question 11

The least positive integer that should besubtracted from 3011$$\times$$3012 so that the different is a perfect square is

Solution

Given expression is 3011$$\times$$3012

If we consider a= 3011, we get a(a+1). To make this a perfect square, we have to subtract it by a, then it becomes

$$ a(a+1) - a $$ = $$ a^2 + a - a $$ = $$ a^2 $$

Therefore, 3011$$\times$$3012 will become a perfect square when it's subtracted by 3011.

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