Question

Simplify the square root of 128

Answer 1

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}}

Explanation: