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Section 1.3 : Radicals
For problems 1 – 4 write the expression in exponential form.
- \(\sqrt[7]{y}\) Solution
- \(\sqrt[3]{{{x^2}}}\) Solution
- \(\sqrt[6]{{ab}}\) Solution
- \(\sqrt {{w^2}{v^3}} \) Solution
For problems 5 – 7 evaluate the radical.
For problems 8 – 12 simplify each of the following. Assume that x, y and z are all positive.
- \(\sqrt[3]{{{x^8}}}\) Solution
- \(\sqrt {8{y^3}} \) Solution
- \(\sqrt[4]{{{x^7}{y^{20}}{z^{11}}}}\) Solution
- \(\sqrt[3]{{54{x^6}{y^7}{z^2}}}\) Solution
- \(\sqrt[4]{{4{x^3}y}}\,\,\sqrt[4]{{8{x^2}{y^3}{z^5}}}\) Solution
For problems 13 – 15 multiply each of the following. Assume that x is positive.
- \(\sqrt x \left( {4 - 3\sqrt x } \right)\) Solution
- \(\left( {2\sqrt x + 1} \right)\left( {3 - 4\sqrt x } \right)\) Solution
- \(\left( {\sqrt[3]{x} + 2\,\,\sqrt[3]{{{x^2}}}} \right)\left( {4 - \sqrt[3]{{{x^2}}}} \right)\) Solution
For problems 16 – 19 rationalize the denominator. Assume that x and y are both positive.