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Mathematics
Donavan
17 December, 18:59
Simplify the square root of 128
+2
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1
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Melina Moody
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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