Real Numbers Quiz Part 1: Mastery Mode

Out of the following sums, which is the greatest?

If a = \( \frac{\sqrt{80}+\sqrt{45}}{{7}} \) and b=\( \sqrt{125}-2\sqrt{20} \), then:

\( \sqrt{ \frac{\sqrt{18}+\sqrt{6}}{\sqrt{18}-\sqrt{6}}-(81^{\frac{1}{4}})^{\frac{1}{2}}} \)

\( \frac{\sqrt{50}-\sqrt{18}+\sqrt{32}}{((2^2)^{\frac{1}{2}})^2 +1+((2^{76})^0)^{52}}\)

\( \sqrt[3]{\frac{(4\sqrt{2})^{2}}{4}} \)

\( \sqrt{(\sqrt{17}+1) \times (\sqrt{17}-1)} \)

\( \sqrt{\sqrt[3]{\sqrt[4]{\sqrt[5]{4^{60}}}}} \)

\( \sqrt{\sqrt{\sqrt{16}*36}+\sqrt{13\sqrt{169}}} \)

\( \frac{\frac{(\frac{9}{4})^{-\frac{5}{2}}}{(\frac{2}{3})^{-3}}{(\frac{1}{3})^{-2}}} + \frac{\frac{9}{16})^{-\frac{2}{3}}}{(\frac{9}{4})^{\frac{1}{2}}} \)

\( \frac{9*9^{2^{4}}\sqrt{9^9+9^9+9^9+9^9+9^9+9^9+9^9+9^9+9^9}}{9\div 9\div 9\div 9\div 9\div 9\div 9\div 9\div 9} \)

Which is the largest number?

\( \frac{\sqrt{7} \times \sqrt{7} \times \sqrt{7} \times \sqrt{7} \times \sqrt{7} \times \sqrt{7} \times \sqrt{7}}{\sqrt{7} + \sqrt {7} + \sqrt{7} + \sqrt {7} + \sqrt{7} + \sqrt {7} +\sqrt{7}}=\)

\( \frac{\sqrt[9]{4^{40}+2^{80}}}{\sqrt{8^3-4^4}}=\)

\( \frac{\sqrt{4^6+4^6}}{\sqrt{2^4  \times 2^4 \times 2^4}}=\)