5. \(\left(-\frac3{\sqrt5}\right)^2+\left(\frac{2\sqrt2}{15}\right)^2-\frac{\sqrt{125}}{\sqrt5}+\left(\frac{2\sqrt2}{\sqrt3}\right)^2\)

Question

Вопрос:

5. \(\left(-\frac3{\sqrt5}\right)^2+\left(\frac{2\sqrt2}{15}\right)^2-\frac{\sqrt{125}}{\sqrt5}+\left(\frac{2\sqrt2}{\sqrt3}\right)^2\)

Accepted Answer

Вычислим каждое слагаемое: \(\left(-\frac3{\sqrt5}\right)^2=\frac95\), \(\left(\frac{2\sqrt2}{15}\right)^2=\frac8{225}\), \(\frac{\sqrt{125}}{\sqrt5}=5\), \(\left(\frac{2\sqrt2}{\sqrt3}\right)^2=\frac83\).

\[\frac95+\frac8{225}-5+\frac83=\frac{405+8-1125+600}{225}=-\frac{112}{225}.\]

Ответ: \(-\frac{112}{225}\)