Examples -> Algebra -> Roots -> Simplifying

 Exercise 1. [ID:91] [Level: ] [Number of helps: 1] [Number of pictures: 0] [Number of steps: 11] [Number of characters: 0] Evaluate the following expression:$\left(\sqrt[3]{1+2\sqrt{6}}-\sqrt[6]{25+4\sqrt{6}}\right)·\sqrt[3]{2\sqrt{6}-1}$
 Exercise 2. [ID:93] [Level: ] [Number of helps: 1] [Number of pictures: 0] [Number of steps: 10] [Number of characters: 0] Simplify the following expression:${x}^{\frac{2}{3}}·{x}^{\frac{3}{4}}·{x}^{-1}$
 Exercise 3. [ID:95] [Level: ] [Number of helps: 0] [Number of pictures: 0] [Number of steps: 9] [Number of characters: 0] Evaluate the following expression:$\sqrt{6-4\sqrt{2}}$
 Exercise 4. [ID:107] [Level: ] [Number of helps: 0] [Number of pictures: 0] [Number of steps: 9] [Number of characters: 0] Evaluate the following expression:${243}^{\frac{1}{5}}-{\left(\frac{1}{81}\right)}^{\frac{1}{4}}+{\left(92+7,5\right)}^{0}+{\left({9}^{\frac{7}{8}}:{3}^{\frac{5}{4}}\right)}^{4}$
 Exercise 5. [ID:110] [Level: ] [Number of helps: 1] [Number of pictures: 0] [Number of steps: 8] [Number of characters: 0] Prove the truth of equation below.$\sqrt[3]{\frac{{a}^{2}}{b}}·\sqrt[4]{\frac{3{b}^{3}}{5{a}^{3}}}·\sqrt[6]{\frac{5a}{3{b}^{3}}}=\sqrt[8]{\frac{{a}^{2}}{2b}}·\sqrt[12]{\frac{3{b}^{2}}{{a}^{2}}}·\sqrt[24]{\frac{8}{25{b}^{3}}}$
 Exercise 6. [ID:277] [Level: ] [Number of helps: 0] [Number of pictures: 0] [Number of steps: 7] [Number of characters: 0] Solve the following equation.
 Exercise 7. [ID:278] [Level: ] [Number of helps: 0] [Number of pictures: 0] [Number of steps: 14] [Number of characters: 0] Simplify the following expression:$\sqrt{\frac{\left(1+a\right)·\sqrt[3]{1+a}}{3a}}·\sqrt[3]{\frac{\sqrt{3}}{9+18{a}^{-1}+9{a}^{-2}}}$
 Exercise 8. [ID:88] [Level: ] [Number of helps: 0] [Number of pictures: 0] [Number of steps: 5] [Number of characters: 0] Simplify the following expression:$a\sqrt{128}$
 Exercise 9. [ID:97] [Level: ] [Number of helps: 1] [Number of pictures: 0] [Number of steps: 11] [Number of characters: 0] Simplify the following expression:$\sqrt{ab}·\sqrt[6]{{a}^{2}{b}^{3}}·\sqrt[6]{{a}^{9}{b}^{8}}$