Subjective Type

Calculate $$(1001)^{1/3}$$.

Solution

We can write $$1001$$ as $$1001 = 1000\left (1 + \dfrac {1}{1000}\right )$$, so that we have
$$(1001)^{1/3} = \left [1000\left (1 + \dfrac {1}{1000}\right )\right ]^{1/3} = 10 \left [1 + \dfrac {1}{1000}\right ]^{1/3}$$
$$= 10(1 + 0.001)^{1/3} = 10\left (1 + \dfrac {1}{3}\times 0.001\right )$$
$$= 10.003333$$.

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