Question

The value of $\sqrt[2010]{2010(2\sqrt{7}-3\sqrt{3})\sqrt{55+12\sqrt{21}}}$ is

• A. $-1$
• B. $1$
• C. $0$
• D. $2$

Answer 1

Answer: (B)

$1$

Now,

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

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

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

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

$=\sqrt[2010]{201028-27}$

$=\sqrt[2010]{20101}$

$=1$.