Tick (✓) the correct answer

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 .

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