Question

How to find the cube root of any no. by estimation? Please explain with an example.
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Answer 1

to find cube root of any number,just check that whether the number inside cube root would be written into power 3,6 etc.if yes then cube root cancels by that power.
for eg.
$\sqrt[3]{125} = \sqrt[3]{( {5})^{3} } \\ { {5}^{3} }^{ \frac{1}{3} } = 5$
or
$\sqrt[3]{256} \\ = \sqrt[3]{ {2}^{8} } \\ = \sqrt[3]{ {2}^{6} \times {2}^{2} } \\ = { {2}^{6} }^{ \frac{1}{3} } \times \sqrt[3]{4} \\ = 4 \sqrt[3]{4}$