Question

$\sqrt[2010]{20102\sqrt{7}-3\sqrt{3}}\times \sqrt[4020]{402055+12\sqrt{21}}$ is equal to

• A. $-1$
• B. $1$
• C. $0$
• D. $2$

Answer 1

Answer: (B)

$1$

$\Rightarrow$$\sqrt[2010]{20102\sqrt{7}-3\sqrt{3}}\times \sqrt[4020]{402055+12\sqrt{21}}$

$\Rightarrow$$\sqrt[2010]{20102\sqrt{7}-3\sqrt{3}}\times {\sqrt[4020]{4020(2\sqrt{7}+3\sqrt{3})}}^2$

$\Rightarrow$$\sqrt[2010]{20102\sqrt{7}-3\sqrt{3}}\times \sqrt[2010]{20102\sqrt{7}+3\sqrt{3}}$

$\Rightarrow$$\sqrt[2010]{20102\sqrt{7}-3\sqrt{3}(2\sqrt{7}+3\sqrt{3})}=\sqrt[2010]{2010(28-27)}=1$