Ответ:

  1. При \(a=0.47\), \(b=0.34\):
    \(\sqrt{a+b}=\sqrt{0.47+0.34}=\sqrt{0.81}=0.9\).
  2. При \(a=\frac14\), \(b=\frac49\):
    \(\sqrt{a+b}=\sqrt{\frac14+\frac49}=\sqrt{\frac{9+16}{36}}=\sqrt{\frac{25}{36}}=\frac56\).

Ответ: 0,9; \(\frac56\).