Question

Evaluate the expression $5\sqrt[3]{729}–24$ .

Answer 1

Given expression: $5\sqrt[3]{729}–24$.

We know that

$\sqrt[\mathrm{n}]{\mathrm{a}}={\left(\mathrm{a}\right)}^{\frac{1}{\mathrm{n}}}\&{\left({\mathrm{a}}^{\mathrm{m}}\right)}^{\mathrm{n}}={\mathrm{a}}^{\mathrm{m}\times \mathrm{n}}$

Now,

$5\sqrt[3]{729}–24$

Since, $729=9\times 9\times 9={\left(9\right)}^3$

$$\begin{gathered} =5\sqrt[3]{{\left(9\right)}^3}–24 \\ =5{\left(9\right)}^{3\times \frac{1}{3}}-24 \\ =5\times 9-24 \\ =45-24 \\ =21 \end{gathered}$$

Hence, $5\sqrt[3]{729}–24=21$.