Question

Calcule o valor de m = (2√8+3√5-7√2).(√72+√20-4√2)

Answer 1

$(2 \sqrt{8} + 3 \sqrt{5} - 7 \sqrt{2}) .( \sqrt{72} + \sqrt{20} - 4 \sqrt{2}) \\ \\ \\ (2 \sqrt{2^3} + 3 \sqrt{5} - 7 \sqrt{2}).( \sqrt{2^3.3^2 } + \sqrt{2^2.5} - 4 \sqrt{2}}) \\ \\ (4 \sqrt{2} + 3 \sqrt{5} - 7 \sqrt{2}).( 6\sqrt{2 } + 2\sqrt{5} - 4 \sqrt{2}}) \\ \\ (-3 \sqrt{2} + 3 \sqrt{5}) .(2 \sqrt{2} + 2 \sqrt{5}) \\ \\ -3 \sqrt{2}. 2 \sqrt{2} - 3 \sqrt{2}. 2 \sqrt{5} + 3 \sqrt{5}. 2 \sqrt{2} + 3 \sqrt{5}. 2\sqrt{5}$

$-3.2.(\sqrt{2})^2 - 6 \sqrt{10} + 3.2. \sqrt{10} + 3.2.(\sqrt{5})^2 \\ \\ -12 -6 \sqrt{10} + 6 \sqrt{10} + 6.5 \\ \\ -12 + 30 \\ \\ =\ \textgreater \ 18$