Упростите выражение 2√18 + 5√50 − 1/4√32 − 7√2.

Упростим корни:

\(\sqrt{18}=3\sqrt{2}\), \(\sqrt{50}=5\sqrt{2}\), \(\sqrt{32}=4\sqrt{2}\).

Тогда:

\(2\sqrt{18}+5\sqrt{50}-\frac{1}{4}\sqrt{32}-7\sqrt{2}=2\cdot3\sqrt{2}+5\cdot5\sqrt{2}-\frac{1}{4}\cdot4\sqrt{2}-7\sqrt{2}\)

\(=6\sqrt{2}+25\sqrt{2}-\sqrt{2}-7\sqrt{2}=23\sqrt{2}\).

Ответ: \(23\sqrt{2}\).