Question

Simplify the radical expression.. square root of 128

Answer 1

Hello,

first we have to descompose the number:

128 | 2
64 | 2
32 | 2
16 | 2
8 | 2
4 | 2
2 | 2
1

So:

`128= 2x2x2x2x2x2x2 \\ 128=2^(6) *2`

Therefore:

`√(128)= \sqrt{2^(6) *2}`

You must know these properties:


`√(a*b) = √(a) * √(b)\\ \\ \sqrt[b]{x^a}= x^{ (a)/(b)}`

then:


`\sqrt{2^(6) *2} \\ =\sqrt{2^(6)}*√(2) \\ =2^{ (6)/(2)}*√(2) \\ =2^3*√(2) \\ \boxed{=8*√(2)}`