[tex]a)\ \ \sqrt[3]{27}+\sqrt{144}=\sqrt[3]{3^3}+\sqrt{12^2}=3+12=15\\\\b)\ \ \sqrt[3]{9^2+135}=\sqrt[3]{81+135}=\sqrt[3]{216}=\sqrt[3]{6^3}=6\\\\c)\ \ \frac{\sqrt{75}-\sqrt{3} }{\sqrt{3}}=\frac{\sqrt{25\cdot3}-\sqrt{3}}{\sqrt{3}}=\frac{\sqrt{25}\cdot\sqrt{3}-\sqrt{3}}{\sqrt{3}}=\frac{5\sqrt{3}-\sqrt{3}}{\sqrt{3}}=\frac{4\sqrt{\not3}}{\sqrt{\not3}}=4\\\\d)\ \ \sqrt[3]{25}\cdot\sqrt[3]{5}+\sqrt{5}\cdot\sqrt{20}=\sqrt[3]{25\cdot5}+\sqrt{5\cdot20}=\sqrt[3]{125}+\sqrt{100}=\sqrt[3]{5^3}+\sqrt{10^2}=[/tex][tex]=5+10=15\\\\e)\ \ \sqrt[3]{17^3}+\sqrt[3]{2^3}=17+2=19\\\\\\Zastosowano\ \ wlasno\'sci\ \ pierwiastk\'ow\\\\\sqrt{a^2}=a\ \ \ \ dla\ \ a\geq 0\\\\ \sqrt[3]{a^3}=a\ \ \ \ dla\ \ a\geq 0\\\\\sqrt{a}\cdot\sqrt{b}=\sqrt{a\cdot b}\\\\\sqrt[3]{a}\cdot\sqrt[3]{b}=\sqrt[3]{a\cdot b}[/tex]
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[tex]a)\ \ \sqrt[3]{27}+\sqrt{144}=\sqrt[3]{3^3}+\sqrt{12^2}=3+12=15\\\\b)\ \ \sqrt[3]{9^2+135}=\sqrt[3]{81+135}=\sqrt[3]{216}=\sqrt[3]{6^3}=6\\\\c)\ \ \frac{\sqrt{75}-\sqrt{3} }{\sqrt{3}}=\frac{\sqrt{25\cdot3}-\sqrt{3}}{\sqrt{3}}=\frac{\sqrt{25}\cdot\sqrt{3}-\sqrt{3}}{\sqrt{3}}=\frac{5\sqrt{3}-\sqrt{3}}{\sqrt{3}}=\frac{4\sqrt{\not3}}{\sqrt{\not3}}=4\\\\d)\ \ \sqrt[3]{25}\cdot\sqrt[3]{5}+\sqrt{5}\cdot\sqrt{20}=\sqrt[3]{25\cdot5}+\sqrt{5\cdot20}=\sqrt[3]{125}+\sqrt{100}=\sqrt[3]{5^3}+\sqrt{10^2}=[/tex][tex]=5+10=15\\\\e)\ \ \sqrt[3]{17^3}+\sqrt[3]{2^3}=17+2=19\\\\\\Zastosowano\ \ wlasno\'sci\ \ pierwiastk\'ow\\\\\sqrt{a^2}=a\ \ \ \ dla\ \ a\geq 0\\\\ \sqrt[3]{a^3}=a\ \ \ \ dla\ \ a\geq 0\\\\\sqrt{a}\cdot\sqrt{b}=\sqrt{a\cdot b}\\\\\sqrt[3]{a}\cdot\sqrt[3]{b}=\sqrt[3]{a\cdot b}[/tex]