Hello,
first we have to descompose the number:
128 | 2
64 | 2
32 | 2
16 | 2
8 | 2
4 | 2
2 | 2
1
So:
[tex]128= 2x2x2x2x2x2x2 \\ 128=2^{6} *2[/tex]
Therefore:
[tex] \sqrt{128}= \sqrt{2^{6} *2} [/tex]
You must know these properties:
[tex] \sqrt{a*b} = \sqrt{a} * \sqrt{b}\\ \\ \sqrt[b]{x^a}= x^{ \frac{a}{b}} [/tex]
then:
[tex]\sqrt{2^{6} *2} \\ =\sqrt{2^{6}}*\sqrt{2} \\ =2^{ \frac{6}{2}}*\sqrt{2} \\ =2^3*\sqrt{2} \\ \boxed{=8*\sqrt{2}}[/tex]
