Ответ:

  1. При \(a=0.47\), \(b=0.34\):
    \(\sqrt{a+b}=\sqrt{0.47+0.34}=\sqrt{0.81}=0.9\).
  2. При \(a=\frac{1}{4}\), \(b=\frac{4}{9}\):
    \(\sqrt{a+b}=\sqrt{\frac{1}{4}+\frac{4}{9}}=\sqrt{\frac{9+16}{36}}=\sqrt{\frac{25}{36}}=\frac{5}{6}\).

Ответ: 1) 0,9; 2) \(\frac{5}{6}\).