Question

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

Answer 1

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