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Simplify the radical expression.. square root of 128

User Dnyanesh M
by
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1 Answer

4 votes
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:

√(128)= \sqrt{2^(6) *2}

You must know these properties:


√(a*b) = √(a) * √(b)\\ \\ \sqrt[b]{x^a}= x^{ (a)/(b)}

then:


\sqrt{2^(6) *2} \\ =\sqrt{2^(6)}*√(2) \\ =2^{ (6)/(2)}*√(2) \\ =2^3*√(2) \\ \boxed{=8*√(2)}
User Falko Menge
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7.9k points