Simplify the square root of 128

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}}