Algebra

 

What is the smallest positive integer n such that \sqrt[4]{675 + n} is an integer?    

 

I think the problem is asking for the square root of the quantity [ (4) • (675 + n) ]    

 

If so, I observe that 676 is a perfect square, and so is 4.    

 

So, we just need to assign n the value 1 to obtain sqrt(2704) which is 52.