Consider a few powers which are close to 120 and 130:
squares:
[tex]10^2=100\\\\ 11^2=121\\\\12^2=144[/tex]
cubes:
[tex]3^3=27\\\\4^3=64\\\\5^3=125\\\\6^3=216[/tex]
4th powers:
[tex]3^4=81\\\\4^4=256[/tex]
now clearly there is no point of checking 5th, 6th and so on powers of numbers >2.
so check powers of 2:
[tex]2^5=32, 2^6=64, 2^7=128[/tex]
So we have :
[tex]11^2=121\\\\5^3=125\\\\2^7=128[/tex]
