Question

Вычеслить:
$5sqrt{3 sqrt{32} } -7 sqrt{15 sqrt{50} }-4 sqrt{6 sqrt{128} }$

Answer 1

$5sqrt{3sqrt{32}}-7sqrt{15sqrt{50}}-4sqrt{6sqrt{128}}=\\=5sqrt{3sqrt{16cdot2}}-7sqrt{15sqrt{25cdot2}}-4sqrt{6sqrt{64cdot 2}}=\\=5sqrt{3sqrt{4^2cdot2}}-7sqrt{15sqrt{5^2cdot2}}-4sqrt{6sqrt{8^2cdot 2}}=\\=5sqrt{3cdot4sqrt{2}}-7sqrt{15cdot5sqrt{2}}-4sqrt{6cdot8sqrt{2}}=\\=5sqrt{3cdot4sqrt{2}}-7sqrt{3cdot 5cdot5sqrt{2}}-4sqrt{3cdot2cdot8sqrt{2}}=\\=5sqrt{3cdot2^2sqrt{2}}-7sqrt{3cdot5^2sqrt{2}}-4sqrt{3cdot4^2sqrt{2}}=$
$=5cdot 2sqrt{3sqrt{2}}-7cdot 5sqrt{3sqrt{2}}-4cdot4sqrt{3sqrt{2}}=\\=10sqrt{3sqrt{2}}-35sqrt{3sqrt{2}}-16sqrt{3sqrt{2}}=-41sqrt{3sqrt2}.$