Question

how do you solve this:

the square root of a+4 plus the square root of a-3 equals 7

Answer 1

sqrt (a+4) + sqrt (a-3)=7

with seven on the right, the sqrt have to add to integers, which means each is an integer.

So a has to be an integer, and a+4 and a-3 is an integer with a ingeter square root.

Possible a:
Start with 1, and see if a-4 and a-3 have integer square roots. It wont take you more than 20 seconds to find it.