11×11 = 121 = 171 in base 8
read here on how to convert one number from 10 base to another base
by following that:
121/8 = 15 R 1
15/8 = 1 R 7

= 1*8^2 + 7*8^1 + 1*8^0 = 171

thus 15×15 = 225
225/8 = 28 R 1
28/8 = 3 R 4
= 3*8^2 + 4*8^1 + 1*8^0 = 341

OR you can try this online tool to convert the base

Answer courtsey: George Georgiev