15.7. а) \(\sqrt{1\frac{7}{9}\cdot\frac{4}{25}}\); б) \(\sqrt{3\frac{1}{16}\cdot2\frac{14}{25}}\).

1. \(1\frac{7}{9}=\frac{16}{9}\). Тогда \(\sqrt{1\frac{7}{9}\cdot\frac{4}{25}}=\sqrt{\frac{16}{9}\cdot\frac{4}{25}}=\sqrt{\frac{64}{225}}=\frac{8}{15}\).
2. \(3\frac{1}{16}=\frac{49}{16}\), а \(2\frac{14}{25}=\frac{64}{25}\). Тогда \(\sqrt{3\frac{1}{16}\cdot2\frac{14}{25}}=\sqrt{\frac{49}{16}\cdot\frac{64}{25}}=\sqrt{\frac{196}{25}}=\frac{14}{5}\).

Ответ: а) \(\frac{8}{15}\); б) \(\frac{14}{5}\).