Barbara20
Answered

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Simplify the radical expression.. square root of 128

Sagot :

Illuminati750
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]
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