Question

Tick (✓) the correct answer
$\sqrt[3]{125\times 64}=?$
(a) 100
(b) 40
(c) 20
(d) 30

Answer 1

(c) 20

$\sqrt[3]{125\times 64}=\sqrt[3]{125}\times \sqrt[3]{64}=\sqrt[3]{5\times 5\times 5}\times \sqrt[3]{2\times 2\times 2\times 2\times 2\times 2}$
$\sqrt[3]{125\times 64}=\sqrt[3]{{\left(5\right)}^3}\times \sqrt[3]{{\left(2\right)}^3\times {\left(2\right)}^3}=\sqrt[3]{{\left(5\right)}^3}\times \sqrt[3]{{\left(4\right)}^3}$
$\sqrt[3]{125\times 64}=5\times 4=20$

Hence, the cube root of $\sqrt[3]{125\times 64}$ is 20.