Question

Simplify: $\sqrt[6]{615-2\sqrt{56}}\sqrt[3]{3\sqrt{7}+2\sqrt{2}}$

• A. $8$
• B. $7$
• C. $2$
• D. $1$

Answer 1

The correct option is D $1$

$\sqrt[6]{615-2\sqrt{56}}\sqrt[3]{3\sqrt{7}+2\sqrt{2}}$

$=\sqrt[6]{615-2\sqrt{56}}\sqrt[6]{6(\sqrt{7}+2\sqrt{2}{)}^2}$

$=\sqrt[6]{615-2\sqrt{56}}\sqrt[6]{615+4\sqrt{14}}$

$=\sqrt[6]{615-2\sqrt{56}}\sqrt[6]{615+2\sqrt{56}}$

$=\sqrt[6]{6225-224}=1$