Question

Надо упростить выражение (8√18+6√24-√72):2√6

Answer 1

$\frac{8\sqrt{18} + 6 \sqrt{24} - \sqrt{72} }{2 \sqrt{6} } = \frac{8\sqrt{9*2} + 6 \sqrt{6*4} - \sqrt{9*4*2} }{2 \sqrt{6} } = \frac{8*3\sqrt{2} + 6*2 \sqrt{6} - 3*2\sqrt{2} }{2 \sqrt{6} } =$
$\frac{24\sqrt{2} + 12 \sqrt{6} - 6\sqrt{2} }{2 \sqrt{6} } = \frac{18\sqrt{2} + 12 \sqrt{6} }{2 \sqrt{6} } = \frac{18\sqrt{2} }{2 \sqrt{6} } + \frac{ 12 \sqrt{6} }{2 \sqrt{6} } = \sqrt{ \frac{648}{24} } + 6 = \sqrt{27} + 6 =$
$= \sqrt{9*3} + 6 = 3 \sqrt{3} + 6$