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17 December, 18:59

Simplify the square root of 128

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Answers (1)
  1. 17 December, 19:14
    0
    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}}
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