Question

Quais são os resultados dessas questões?

Answer 1

$a) \, \sqrt{2} ( \sqrt{2} + \sqrt{3} ) = \sqrt{2} .\sqrt{2} + \sqrt{2} . \sqrt{3} =\\ = (\sqrt{2})^2 + \sqrt{2.3} = 2+ \sqrt{6}$

$b)\, \sqrt{5} . (1- \sqrt{3}) = \sqrt{5} .1 + \sqrt{5}.(- \sqrt{3}) =\\ \,\, = \sqrt{5} - \sqrt{5.3} = \sqrt{5} - \sqrt{15}$

$c)\,\, (2 \sqrt{3} + 3 \sqrt{6} )2 \sqrt{3} = \\ 2 \sqrt{3}.2 \sqrt{3} + 3 \sqrt{6}.2 \sqrt{3}=\\ 4 (\sqrt{3})^2 +6 \sqrt{6.3} = 4.3 + \sqrt{2}.18 \\ =12+ 18\sqrt{2}$

$d)\,\, ( \sqrt{2} + \sqrt{3} ) x^{2} = (\sqrt{2} )^2+2. \sqrt{2} . \sqrt{3} + ( \sqrt{3} )^2\\ = 2+2 \sqrt{6} + 3\\ = 5+ 2\sqrt{6}$

$e)\,\, ( \sqrt{5} - \sqrt{2} )^2 = ( \sqrt{2} )^2-2. \sqrt{5} . \sqrt{2} +( \sqrt{2} )^2\\ =5 - 2 \sqrt{10} +2\\ = 7-2 \sqrt{10}$