Question

Write in simplest radical form: √208

Answer 1

`208:2=104\\104:2=52\\52:2=26\\26:2=13\\13:13=1\\\\208=2\cdot2\cdot2\cdot2\cdot13=2^2\cdot2^2\cdot13\\\\√(208)=√(2^2\cdot2^2\cdot13)=√(2^2)\cdot√(2^2)\cdot√(13)=2\cdot2\cdot√(13)=4√(13)\\\\Answer:\ √(208)=4√(13)\\\\Used:\\√(ab)=√(a)\cdot√(b)\\\\√(a^2)=a`