The value of 27−332010.55+12214020=

The value of $\sqrt[2010]{2 \sqrt{7} - 3 \sqrt{3}} . \sqrt[4020]{55 + 12 \sqrt{21}} =$

A
0
B
2
C
1
D
3

Solution:

$\sqrt[2010]{2 \sqrt{7} - 3 \sqrt{3}} . \sqrt[4020]{55 + 12 \sqrt{21}}$

$= \sqrt[2010]{2 \sqrt{7} - 3 \sqrt{3}} . \sqrt[2010]{\sqrt[2]{55 + 2 \sqrt{36 \times 21}}}$

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

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

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