Question

Find the cube root of the following number: $(-125)\times (-3375)$.

• A. 25
• B. 55
• C. 35
• D. 75

Answer 1

The correct option is D 75

$-125=-1\times 5\times 5\times 5=-1\times 5^3$

$-3375=-1\times 3\times 3\times 3\times 5\times 5\times 5=-1\times 3^3\times 5^3$
$\therefore 125\times 3375=-1\times -1\times 5^3\times 3^3\times 5^3=1\times 5^3\times 3^3\times 5^3$

Cube root of (-125) x (-3375) is:
$\sqrt[3]{3(-125)\times (-3375)}=\sqrt[3]{35^3\times 3^3\times 5^3}=5\times 3\times 5=75$