First, let's recall that rational numbers can all be expressed as a ratio of two integers. For example, the number 3 can be expressed as the ratios 3/1, 6/2, etc. The number 1/3 is also rational, even though when divided, it is non-terminating (goes on forever) 0.33333....rational numbers may be non-terminating, as long as they are repeating.
Let's first look at the nature of the three given numbers:
32 + n. n can be any integer and the answer will be rational.
n/8. n can be any integer and the answer will be rational (0/8=0, and zero is a rational number)
So, our only term we have to think about is √(n+225). The smallest value that can be solved under a square root is also zero: √0 = 0.
Therefore, let's make n=(-225) and try it out:
32+(-225)=(-193). [rational]
(-225)/8 = (28.125) [rational]
√(-225+225) = √0=0 [rational]
Therefore, n=(-225)
