[tex] \sqrt{(3 \sqrt{5} - 5 \sqrt{3} ) {}^{2} } + \sqrt{(5 - 2 \sqrt{3}) {}^{2} } - \sqrt{(4 \sqrt{5} - 7 \sqrt{3}) {}^{2} } + ( \sqrt{2} ) {}^{4} = 5 \sqrt{3} - 3 \sqrt{5} + 2 \sqrt{3} - \sqrt{5} - (7 \sqrt{3} - 4 \sqrt{5} ) + 2 {}^{2} = 5 \sqrt{3} - 3 \sqrt{5} + 2 \sqrt{3} - \sqrt{5} - 7 \sqrt{3} + 4 \sqrt{5} + 4 = 0 + 0 + 4 = 4[/tex]
