№ 2. Вычислить без помощи микрокалькулятора: a) \(\\( \sqrt[4]{\frac{15}{8}} : \frac{\sqrt{2}}{\sqrt{5}}\)) б) \(\\( \sqrt[3]{\frac{23}{64}} + \sqrt{\frac{5}{48^2 - 32^2}}\))

Решение:

1. \(\\(
   \sqrt[4]{\frac{15}{8}} : \frac{\sqrt{2}}{\sqrt{5}}\)) = \(\\(
   \frac{\sqrt[4]{15}}{\sqrt[4]{8}} · \frac{\sqrt{5}}{\sqrt{2}}\)) = \(\\(
   \frac{\sqrt[4]{15}}{2^{3/4}} · \frac{5^{1/2}}{2^{1/2}}\)) = \(\\(
   \frac{\sqrt[4]{15} · \sqrt{5}}{2^{3/4} · 2^{1/2}}\)) = \(\\(
   \frac{\sqrt[4]{15} · \sqrt[4]{25}}{2^{3/4+1/2}}\)) = \(\\(
   \frac{\sqrt[4]{375}}{2^{5/4}}\))
2. \(\\(
   \sqrt[3]{\frac{23}{64}} +
   \sqrt{\frac{5}{48^2 - 32^2}}\)) = \(\\(
   \frac{\sqrt[3]{23}}{4} +
   \sqrt{\frac{5}{(48-32)(48+32)}}\)) = \(\\(
   \frac{\sqrt[3]{23}}{4} +
   \sqrt{\frac{5}{16 · 80}}\)) = \(\\(
   \frac{\sqrt[3]{23}}{4} +
   \sqrt{\frac{5}{1280}}\)) = \(\\(
   \frac{\sqrt[3]{23}}{4} +
   \sqrt{\frac{1}{256}}\)) = \(\\(
   \frac{\sqrt[3]{23}}{4} + \frac{1}{16}}\))

Ответ: \(\\(
\frac{\sqrt[4]{375}}{2^{5/4}}\)) ; \(\\(
\frac{\sqrt[3]{23}}{4} + \frac{1}{16}}\))