| \(\mathbf{a)}\) | \((3\sqrt{2}+2\sqrt{3})^2\) | \(\mathbf{b)}\) | \((\sqrt{5}-2\sqrt{15})^2\) | |||||
| \(\mathbf{c)}\) | \((2\sqrt{3}-4\sqrt{5})^2\) | \(\mathbf{d)}\) | \((3\sqrt{6}+5\sqrt{3})^2\) | |||||
| \(\mathbf{e)}\) | \((1-\sqrt{3})^2(2+\sqrt{3})\) | \(\mathbf{a)}\) | \((1-\sqrt{2})^2(3+2\sqrt{2})\) | |||||
\(\mathbf{2.}\:\:\) Racionaliziraj nazivnik u razlomku:
| \(\mathbf{a)}\) | \(\frac{1}{\sqrt{3}-\sqrt{2}}\) | \(\mathbf{b)}\) | \(\frac{1}{\sqrt{7}-\sqrt{6}}\) | |||||
| \(\mathbf{c)}\) | \(\frac{\sqrt{3}+\sqrt{5}}{\sqrt{3}-\sqrt{5}}\) | \(\mathbf{d)}\) | \(\frac{\sqrt{7}+\sqrt{3}}{\sqrt{7}-\sqrt{3}}\) | |||||
| \(\mathbf{e)}\) | \(\frac{2\sqrt{7}+7\sqrt{2}}{2\sqrt{7}-7\sqrt{2}}\) | \(\mathbf{a)}\) | \(\frac{\sqrt{x}-\sqrt{y}}{\sqrt{x}+\sqrt{y}}\) | |||||
\(\mathbf{3.}\:\:\) Uradi naznačeno:
\(\mathbf{a)}\) Izračunaj i rezultat djlimično korijenuj
| \(\mathbf{1)}\) | \(\sqrt{3}\cdot\sqrt[3]{9};\) | \(\mathbf{2)}\) | \(\sqrt{5}\cdot\sqrt[3]{625};\) | |||||
| \(\mathbf{3)}\) | \(\sqrt[3]{4}\cdot\sqrt[4]{48};\) | \(\mathbf{4)}\) | \(\sqrt{7}\cdot\sqrt[5]{49}\cdot\sqrt[4]{7};\) | |||||
\(\mathbf{b)}\) Pomnoži:
| \(\mathbf{1)}\) | \(\sqrt[5]{x}\cdot\sqrt[6]{x};\) | \(\mathbf{2)}\) | \(\sqrt[3]{a^2}\cdot\sqrt{a^3};\) | |||||
| \(\mathbf{3)}\) | \(\sqrt{a}\cdot\sqrt[3]{a}\cdot\sqrt[4]{a};\) | \(\mathbf{4)}\) | \(\sqrt{x}\cdot\sqrt[4]{x}\cdot\sqrt[8]{x};\) | |||||
\(\mathbf{4.}\:\:\) Izvedi naznačene operacije.
| \(\mathbf{a)}\) | \(\sqrt[5]{a^2}:\sqrt[4]{a};\) | \(\mathbf{b)}\) | \(\sqrt[5]{x^7y^6}:\sqrt[4]{y^2x^{-3}};\) | |||||
| \(\mathbf{c)}\) | \((\sqrt[3]{9}-2\sqrt{3})\cdot\sqrt[3]{3};\) | \(\mathbf{d)}\) | \((2\sqrt[6]{8}-\sqrt[4]{32}):\sqrt[4]{2};\) | |||||
\(\mathbf{5.}\:\:\) Svedi na potencije s racionalnim eksponentom i izračunaj:
| \(\mathbf{a)}\) | \(\sqrt[4]{\frac{2}{3}a}\cdot \sqrt[6]{\frac{9}{4a}};\) | \(\mathbf{b)}\) | \(\sqrt[3]{a^4b^{-1}}\cdot \sqrt[4]{a^3b^2}\cdot\sqrt[6]{a^{-3}b^5};\) | |||||
| \(\mathbf{c)}\) | \(\sqrt[5]{a^7b^2}\cdot\sqrt{ab^3}:\sqrt[10]{a^{11}b^{-3}};\) | \(\mathbf{d)}\) | \(\sqrt{xy^7}:\sqrt[3]{x^5y}\cdot\sqrt[5]{x^5y};\) | |||||
\(\mathbf{6.}\:\:\) Odredi rješenja iracionalnih jednadžbi:
| \(\mathbf{a)}\) | \(\sqrt{2x+1}=10;\) | \(\mathbf{b)}\) | \(2\sqrt{2x+2}-5=0;\) | |||||
| \(\mathbf{c)}\) | \(\sqrt{4+x}=2\sqrt{x-5};\) | \(\mathbf{d)}\) | \(\sqrt{5-x}=3\sqrt{x+1};\) | |||||
| \(\mathbf{e)}\) | \(\sqrt{x^2+x-2}=x;\) | \(\mathbf{a)}\) | \(\sqrt{x^2+5x+4}=x+2;\) | |||||
