Question

alculaţi:
radical din 32 (2 radical din 75 - V108) - V27 (V242 - V
128​

Answer 1

 

$\displaystyle\bf\\\sqrt{32}\Big(2\sqrt{75}-\sqrt{108}\Big)-\sqrt{27}\Big(\sqrt{242}-\sqrt{128}\Big)=\\\\=\sqrt{16\times2}\Big(2\sqrt{25\times3}-\sqrt{36\times3}\Big)-\sqrt{9\times3}\Big(\sqrt{121\times2}-\sqrt{64\times2}\Big)=\\\\=4\sqrt{2}\Big(2\times5\sqrt{3}-6\sqrt{3}\Big)-3\sqrt{3}\Big(11\sqrt{2}-8\sqrt{2}\Big)=\\\\=4\sqrt{2}\Big(10\sqrt{3}-6\sqrt{3}\Big)-3\sqrt{3}\Big(11\sqrt{2}-8\sqrt{2}\Big)=\\\\=4\sqrt{2}\Big(4\sqrt{3}\Big)-3\sqrt{3}\Big(3\sqrt{2}\Big)=$

.

$\displaystyle\bf\\=4\sqrt{2}\times4\sqrt{3}-3\sqrt{3}\times3\sqrt{2}=\\\\=16\sqrt{2\times3}-9\sqrt{3\times2}=\\\\=16\sqrt{6}-9\sqrt{6}=\\\\=\boxed{\bf7\sqrt{6}}$