Question

$\sqrt[3]{3333+\sqrt[3]{3987+\sqrt[3]{32197}}}$ is equal to:

• A. $21$
• B. $18$
• C. $7$
• D. $3$

Answer 1

Answer: (C)

$7$

$\sqrt[3]{3333+\sqrt[3]{3987+\sqrt[3]{32197}}}$

$=\sqrt[3]{3333+\sqrt[3]{3987+\sqrt[3]{313\times 13\times 13}}}$ ...[Since, $2197=13\times 13\times 13$]

$=\sqrt[3]{3333+\sqrt[3]{3987+13}}$

$=\sqrt[3]{3333+\sqrt[3]{31000}}$

$=\sqrt[3]{3333+\sqrt[3]{310\times 10\times 10}}$ ...[Since, $1000=10\times 10\times 10$]

$=\sqrt[3]{3333+10}$

$=\sqrt[3]{3343}$

$=\sqrt[3]{37\times 7\times 7}$ ...[Since, $343=7\times 7\times 7$]

$=7$.

Hence, option $C$ is correct.