Question:
Tick (✓) the correct answer
$\sqrt[3]{125 \times 64}=?$
(a) 100
(b) 40
(c) 20
(d) 30
Solution:
(c) 20
$\sqrt[3]{125 \times 64}=\sqrt[3]{125} \times \sqrt[3]{64}=\sqrt[3]{5 \times 5 \times 5} \times \sqrt[3]{2 \times 2 \times 2 \times 2 \times 2 \times 2}$
$\sqrt[3]{125 \times 64}=\sqrt[3]{(5)^{3}} \times \sqrt[3]{(2)^{3} \times(2)^{3}}=\sqrt[3]{(5)^{3}} \times \sqrt[3]{(4)^{3}}$
$\sqrt[3]{125 \times 64}=5 \times 4=20$
Hence, the cube root of $\sqrt[3]{125 \times 64}$ is 20 .