Question

Efectuati calculele:
a.2√3+(7√3-5√3)-√108
b.3√5+2(8√5-6√3)-√80
c.2(3√5-4√5)-(11√5-7√5)
d.3(5√2-6√2)-(13√2-8√2)
e.3(√12-√3)+2(8√3-6√3)-4√3
f.5(√18-√2)-4(3√8-5√2)+6√2
Va rog ajutati-ma dar si daca vreti puteti sa imi explicati cum ati facut!!!

Answer 1

$2 \sqrt{3} + (7 \sqrt{3} - 5 \sqrt{3} - \sqrt{108} = \\ = 2 \sqrt{3} + 2 \sqrt{3} - 6\sqrt{3} = \\ = - 2 \sqrt{3} \\ 3 \sqrt{5} + 2(8 \sqrt{5} - 6 \sqrt{3}) - \sqrt{80} = \\ = 3 \sqrt{5} + 16 \sqrt{5} - 16 \sqrt{3} - 4 \sqrt{5} = \\ = 15 \sqrt{5} - 16 \sqrt{3} \\ 2(3 \sqrt{5} - 4 \sqrt{5} ) - (11 \sqrt{5} - 7 \sqrt{5} ) = \\ = 6 \sqrt{5 } - 8 \sqrt{5} - 5 \sqrt{5} = - 7 \sqrt{5} \\ 3(5 \sqrt{2} - 6 \sqrt{2} ) - (13 \sqrt{2} - 8 \sqrt{2} ) = \\ = 15 \sqrt{2} - 18 \sqrt{2} - 5 \sqrt{2} = - 8 \sqrt{2} \\ ( \sqrt{12} - \sqrt{3} ) - 4(3 \sqrt{8} - 5 \sqrt{2} ) + \\ + 6 \sqrt{2} = (2 \sqrt{3} - \sqrt{3} ) - 4(3 \times \\ \times 2 \sqrt{2} - 5 \sqrt{2} ) + 6 \sqrt{2} = \\ = \sqrt{3} - 24 \sqrt{2} - 5 \sqrt{2} + 6 \sqrt{2} = \\ = \sqrt{3 } - 9 \sqrt{2} + 6 \sqrt{2} = \sqrt{3} - \\ - 15 \sqrt{2} \\ 3( \sqrt{12} - \sqrt{3}) + 2(8 \sqrt{3} - 6 \sqrt{3} ) - \\ - 4 \sqrt{3} = 6 \sqrt{3} - \sqrt{3} + 16 \sqrt{3} - \\ - 6 \sqrt{3} - 4 \sqrt{3} = 11 \sqrt{3} \\ 5( \sqrt{18} - \sqrt{2} ) - 4(3 \sqrt{8} - 5 \sqrt{2} + \\ + 6 \sqrt{2} = 15 \sqrt{2} - 4 \times 6 \sqrt{2} - \\ - 5 \sqrt{2} +6 \sqrt{2} = 15 \sqrt{2} - 24 \sqrt{2} - \\ - 5 \sqrt{2} + 6 \sqrt{2} = - 8 \sqrt{2}$
sper ca te-am ajutat