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:
$\sqrt{128}= \sqrt{2^{6} *2}$

You must know these properties:

$\sqrt{a*b} = \sqrt{a} * \sqrt{b}\\ \\ \sqrt[b]{x^a}= x^{ \frac{a}{b}}$

then:

$\sqrt{2^{6} *2} \\ =\sqrt{2^{6}}*\sqrt{2} \\ =2^{ \frac{6}{2}}*\sqrt{2} \\ =2^3*\sqrt{2} \\ \boxed{=8*\sqrt{2}}$