Question

Calcule o valor da expressão 2√8 + 3√5 - 7√2 +√72 +√20 - 4√2

Answer 1

Explicação passo-a-passo:

$2\sqrt{8} +3\sqrt{5} -7\sqrt{2} +\sqrt{72} +\sqrt{20} -4\sqrt{2} =\\ \\ 2\sqrt{2^2.2} +3\sqrt{5} -7\sqrt{2} +\sqrt{2^2.2.3^2}+\sqrt{2^2.5} -4\sqrt{2} =\\ \\ 2.2\sqrt{2} +3\sqrt{5} -7\sqrt{2} +2.3\sqrt{2} +2\sqrt{5} -4\sqrt{2} =\\ \\ 4\sqrt{2} +3\sqrt{5} -7\sqrt{2} +6\sqrt{2} +2\sqrt{5} -4\sqrt{2} =\\ \\ 4\sqrt{2} +6\sqrt{2} -7\sqrt{2} -4\sqrt{2} +3\sqrt{5} +2\sqrt{5} =\\ \\ 10\sqrt{2} -11\sqrt{2} +5\sqrt{5} =\\ \\ -\sqrt{2} +5\sqrt{5}$