Question

Evaluate: $125\sqrt[3]{3a^6}-\sqrt[3]{3125a^6}$

• A. $200a^3$
• B. $a^3$
• C. $120a^2$
• D. $20a$

Answer 1

The correct option is C $120a^2$

Given : $125\sqrt[3]{3a^6}-\sqrt[3]{3125a^6}$

$125\sqrt[3]{3a^6}-\sqrt[3]{3125a^6}=125\sqrt[3]{3(a^2{)}^3}-\sqrt[3]{35\times 5\times 5\times (a^2{)}^3}=125\times \left(a^2\right)-5\left(a^2\right)=125a^2-5a^2=120a^2$

Hence, $125\sqrt[3]{3a^6}-\sqrt[3]{3125a^6}=120a^2$