Question

find cube root by estimation 5832

Answer 1

Given number $5832=18\times 18\times 18$
$\Rightarrow 5832={18}^3$
Taking cube root on both sides, we get
$\Rightarrow \sqrt[3]{35}832=\sqrt[3]{31}{8}^3$
$={\left({18}^3\right)}^{\frac{1}{3}}$ [Since, $\sqrt[n]{nx}=x^{\frac{1}{n}}$]
$={18}^1$ [Since, $(a^m{)}^n=a^{m\times n}$]
$\therefore \sqrt[3]{35}832=18$