Question

simplify the following

Answer 1

here is your 1st 2nd and 3rd answer

Answer 2

i)
$(4 \sqrt{3} - 2 \sqrt{2} )(3 \sqrt{2} + 4 \sqrt{3} ) \\ = 4 \sqrt{3} \times 3 \sqrt{2} + 4 \sqrt{3} \times 4 \sqrt{3} \\ - 2 \sqrt{2} \times 3 \sqrt{2} - 2 \sqrt{2} \times 4 \sqrt{3} \\ = 12 \sqrt{6} + 48 - 12 - 8 \sqrt{6} \\ = 4 \sqrt{6} + 36$
ii)
$(2 + \sqrt{3} )( 3 + \sqrt{5}) \\ = 2 \times3 + 2 \times \sqrt{5} + \sqrt{3} \times 3 + \sqrt{3} \times \sqrt{5} \\ = 6 + 2 \sqrt{5} + 3 \sqrt{3} + \sqrt{15}$
iii)
$( \sqrt{3} + \sqrt{2} ) {}^{2} \\ = (\sqrt{3}) {}^{2} + (\sqrt{2}) {}^{2} + 2 \times \sqrt{ 3} \times \sqrt{2} \\ = 3 + 2 + 2 \sqrt{6 } \\ = 5 + 2 \sqrt{6}$
iv)
$( \frac{2}{3} \sqrt{7} - \frac{1}{2} \sqrt{2} + 6 \sqrt{11} )( \frac{1}{3} \sqrt{7} + \frac{3}{2} \sqrt{2} - \sqrt{11}) \\ = \frac{2}{3} \sqrt{7} \times \frac{1}{3} \sqrt{7} + \frac{2}{3} \sqrt{7} \times \frac{3}{2} \sqrt{2} - \frac{2}{3} \sqrt{7} \times \sqrt{11} \\ - \frac{1}{2} \sqrt{2} \times \frac{1}{3} \sqrt{7} - \frac{1}{2} \sqrt{2} \times \frac{3}{2} \sqrt{2} + \frac{1}{2} \sqrt{2} \times \sqrt{11} \\ + 6 \sqrt{11} \times \frac{1}{3} \sqrt{7} + 6 \sqrt{11} \times \frac{3}{2} \sqrt{2} - 6 \sqrt{11} \times \sqrt{11} \\ = \frac{14}{3} + \sqrt{14} - \frac{2}{3} \sqrt{77 } - \frac{1}{6} \sqrt{14} - \frac{3}{2} + \frac{1}{2} \sqrt{22} \\ + 2 \sqrt{77} + 9 \sqrt{22} - 66 \\ = \frac{14}{3} - \frac{3}{2} - 66 + \sqrt{14} - \frac{1}{6} \sqrt{14} - \frac{2}{3} \sqrt{77} + 2 \sqrt{77} \\ + \frac{1}{2} \sqrt{22} + 9 \sqrt{22} \\ = \frac{ - 377}{6} + \frac{5}{6} \sqrt{14} + \frac{4}{3} \sqrt{77 } + \frac{19}{2} \sqrt{22}$