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:
\(\sqrt{2^{6} *2} \\ =\sqrt{2^{6}}*\sqrt{2} \\ =2^{ \frac{6}{2}}*\sqrt{2} \\ =2^3*\sqrt{2} \\ \boxed{=8*\sqrt{2}}\)
