Zadanie 12
Oblicz:
a) \(\displaystyle \sqrt{64} + \sqrt[3]{1000}\)
b) \(\displaystyle \sqrt[3]{7^2 + 15}\)
c) \(\displaystyle \sqrt{13^2} + \sqrt[3]{7^3}\)
d) \(\displaystyle \sqrt{2} \cdot \sqrt{18} + 3 \cdot \sqrt[3]{3} \cdot \sqrt[3]{9}\)
e) \(\displaystyle \frac{\sqrt{75} + 2\sqrt{3}}{\sqrt{3}}\)
RozwiÄ…zanie:
a)
\[\sqrt{64} + \sqrt[3]{1000} = 8 + 10 = 18\]
b)
\[\sqrt[3]{7^2 + 15} = \sqrt[3]{49 + 15} = \sqrt[3]{64} = 4\]
c)
\[\sqrt{13^2} + \sqrt[3]{7^3} = 13 + 7 = 20\]
d)
\[\sqrt{2} \cdot \sqrt{18} + 3 \cdot \sqrt[3]{3} \cdot \sqrt[3]{9}\]
\[\sqrt{36} + 3 \cdot \sqrt[3]{27}\]
\[6 + 3 \cdot 3 = 6 + 9 = 15\]
e)
\[\frac{\sqrt{75} + 2\sqrt{3}}{\sqrt{3}}\]
\[\sqrt{75} = \sqrt{25 \cdot 3} = 5\sqrt{3}\]
\[\frac{5\sqrt{3} + 2\sqrt{3}}{\sqrt{3}} = \frac{7\sqrt{3}}{\sqrt{3}} = 7\]
Wyniki zadania 12:
a) \(\displaystyle 18\)
b) \(\displaystyle 4\)
c) \(\displaystyle 20\)
d) \(\displaystyle 15\)
e) \(\displaystyle 7\)
a) \(\displaystyle 18\)
b) \(\displaystyle 4\)
c) \(\displaystyle 20\)
d) \(\displaystyle 15\)
e) \(\displaystyle 7\)