oblicz

[NieDlaOka37]

Wiedząc, że \(\sqrt{x}=16,\) \(\sqrt[3]{y} =\frac{1}{2}\) oblicz \(\sqrt[5]{xy}\).

[Szimi10]

\(\sqrt x = 16\\
x=256\)

\(\sqrt[3]{y}=\frac{1}{2}\\
y=\frac{1}{8}\)

\(\sqrt[5]{xy}=\sqrt[5]{256 \cdot \frac{1}{8}}=\sqrt[5]{32}=2\)

Pozdrawiam
Szymon.

[jola]

\(\begin{cases} \sqrt{x}=16\ \ \Rightarrow \ \ x=16^2=2^8\\ \sqrt[3]{y}= \frac{1}{2}\ \ \ \Rightarrow \ \ \ y=2_{-3} \end{cases}\ \ \ \ \Rightarrow \ \ \ \ \sqrt[5]{xy}=(xy)^{ \frac{1}{5}}=(2^8 \cdot 2^{-3})^{ \frac{1}{5}}=(2^5)^{ \frac{1}{5}}=2\)