209k views
2 votes
Simplify the square root of 128

1 Answer

6 votes

Answer:

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:

User Mike Saull
by
8.0k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories