(a) \(\sqrt[\scriptstyle 3]{125}\cdot\sqrt[\scriptstyle 7]{128}\)
(b) \(\sqrt[\scriptstyle 4]{3^8}+\sqrt[\scriptstyle 6]{3^0}\)
(c) \(\sqrt[\scriptstyle 3]{250~\sqrt[\scriptstyle 3]{(-8)^2}}\)
Rešitev: (a) \(\cdots=10\), (b) \(\cdots=10\), (c) \(\cdots=10\)(a) \(8\raise0.9em{\textstyle\frac{2}{3}}+9\raise0.9em{\textstyle\frac{3}{2}}\)
(b) \(\Big(27\raise0.9em{-\textstyle\frac{1}{3}}+6^{-1}\Big)\cdot 16\raise0.9em{\textstyle\frac{1}{4}}\)
(c) \(\Big(6\frac{1}{4}\Big)\raise0.9em{-\textstyle\frac{1}{2}}\cdot 125\raise0.9em{\textstyle\frac{2}{3}}\cdot \sqrt{9^{1,5}-2} \)
Rešitev: (a) \(\cdots=31\), (b) \(\cdots=1\), (c) \(\cdots=50\)(a) \({\displaystyle\frac{x^2~(xy^2)^3}{x^6 y~(x^{-1}y)^2}}\)
(b) \({\displaystyle\frac{x y^2 \frac{\textstyle x^5}{\textstyle y^7}} {\frac{\textstyle x y}{\textstyle y^6} (x^{-2})^{-3}}}\)
(c) \({\displaystyle\frac{(2x)^3~y^{-2}}{xy^{-3}}+\frac{(x^3)^5~x^{-13}}{(2y)^{-5}~y^4}}\)
Rešitev: (a) \(\cdots=xy^3\), (b) \(\cdots=x^{-1}=\frac{1}{x}\), (c) \(\cdots=40x^2y\)(a) \({\displaystyle\sqrt[\scriptstyle 3]{64x^{12}y^9}\cdot \sqrt[\scriptstyle 4]{\frac{81y^4}{x^{12}}}}\)
(b) \({\displaystyle\sqrt[\scriptstyle 5]{\frac{-32}{xy^2}\cdot \sqrt[\scriptstyle 3]{x^{18}y^{36}}}}\)
(c) \({\displaystyle\frac{\sqrt[\scriptstyle 3]{\frac{\textstyle \sqrt{x^2}}{\textstyle xy^6}}} {\sqrt[\scriptstyle 4]{\frac{\textstyle xy^{10}}{\textstyle (x^3y^2)^3}}}}\)
Rešitev: (a) \(\cdots=12xy^4\), (b) \(\cdots=-2xy^2\), (c) \(\cdots=x^2y^{-3}=\frac{x^2}{y^3}\)(a) \({\displaystyle\frac{\sqrt{x^5y^3}}{\sqrt[\scriptstyle3]{x^4y^2}~ \sqrt[\scriptstyle6]{xy^2}}}\)
(b) \({\displaystyle\sqrt[\scriptstyle 5]{\frac{243~ \sqrt[\scriptstyle3]{x^5y}~ \sqrt{xy}}{32x^2y~ \sqrt[\scriptstyle6]{xy^{-1}}}}}\)
(c) \({\displaystyle\frac{\sqrt[\scriptstyle4]{x^6y^2}}{\sqrt[\scriptstyle3]{x^4y}} - \sqrt[\scriptstyle3]{\frac{xy}{\sqrt{xy}}}}\)
Rešitev: (a) \(\cdots=x\sqrt{y}\), (b) \(\cdots=\frac{3}{2}\), (c) \(\cdots=0\)(a) \((\sqrt{50}-\sqrt{32})(\sqrt{27}-\sqrt{12})\)
(b) \({\displaystyle\frac{\sqrt{60}-\sqrt{15}}{\sqrt{75}-\sqrt{48}}}\)
(c) \({\displaystyle\frac{\sqrt{125}+\sqrt{9}-\sqrt{20}}{1+\sqrt{80}-\sqrt{45}}}\)
Rešitev: (a) \(\cdots=\sqrt{6}\), (b) \(\cdots=\sqrt{5}\), (c) \(\cdots=3\)(a) \({\displaystyle\frac{12}{\sqrt{6}}}\)
(b) \({\displaystyle\frac{12}{1+\sqrt{5}}}\)
(c) \({\displaystyle\frac{4\sqrt{7}}{3-\sqrt{7}}}\)
Rešitev: (a) \(\cdots=2\sqrt{6}\), (b) \(\cdots=-3+3\sqrt{5}\), (c) \(\cdots=14+6\sqrt{7}\)(a) \({\displaystyle\frac{\sqrt{12}}{1-\frac{\textstyle1}{\textstyle\sqrt{3}}}}\)
(b) \({\displaystyle\Big(\frac{6}{\sqrt{2}} -\sqrt{8}\Big)^6 }\)
Rešitev: (a) \(\cdots=3+3\sqrt{3}\), (b) \(\cdots=8\)(a) \(x^5=32\)
(b) \(x^4=81\)
(c) \((x-2)^3=125\)
(d) \((2x+3)^4=625\)
Rešitev: (a) \(x=2\), (b) \(x_1=3,~ x_2=-3\), (c) \(x=7\), (d) \(x_1=1,~ x_2=-4\)(a) \(4x^2=1\)
(b) \(2x^3+54=0\)
(c) \(3x^4+3=0\)
(d) \((x^3-13)^2-196=0\)
Rešitev: (a) \(x_1=\frac{1}{2},~ x_2=-\frac{1}{2}\), (b) \(x=-3\), (c) enačba ni rešljiva v \(\mathrm{I\!R}\), (d) \(x_1=-1,~ x_2=3\)(a) \(\sqrt[\scriptstyle3]{x}=4\)
(b) \(\sqrt[\scriptstyle4]{x+10}=2\)
(c) \(\sqrt[\scriptstyle5]{6x-2}=-2\)
Rešitev: (a) \(x=64\), (b) \(x=6\), (c) \(x=-5\)(a) \(\sqrt[\scriptstyle3]{x-2}-2=0\)
(b) \(\sqrt[\scriptstyle4]{2x-5}+3=0\)
(c) \({\displaystyle5-\sqrt{\frac{x+3}{2}}=0}\)
Rešitev: (a) \(x=10\), (b) enačba ni rešljiva v \(\mathrm{I\!R}\), (c) \(x=47\)(a) \(\big(1+\sqrt[\scriptstyle3]{x+2}\big)^3=27\)
(b) \(\sqrt[\scriptstyle3]{(x-2)^4-17}=4\)
(c) \({\displaystyle\frac{1+\sqrt{4+\sqrt[\scriptstyle3]{2x+5}}}{4}=1}\)
Rešitev: (a) \(x=6\), (b) \(x_1=5,~ x_2=-1\), (c) \(x=60\)(a) \(\sqrt{x^2-5}=x-1\)
(b) \(x+\sqrt{x^2-6x}=2\)
(c) \(x+\sqrt{2x+1}=1\)
(d) \(3+\sqrt{2x+2}=x\)
Rešitev: (a) \(x=3\), (b) \(x=-2\), (c) \(x=0\), (d) \(x=7\)(a) \(\sqrt[\scriptstyle3]{x^2-1}=x-1\)
(b) \(1+\sqrt[\scriptstyle3]{x^3-4x^2+39}=x\)
Rešitev: (a) \(x_1=0,~x_2=1,~x_3=3\), (b) \(x_1=-8,~x_2=5\)(a) \(f_1(x)=x^2\)
(b) \(f_2(x)=\frac{1}{2}x^2\)
(c) \(f_3(x)=\frac{1}{2}x^2-3\)
