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Section 1-3 : Radicals

For problems 1 – 4 write the expression in exponential form.

  1. \(\sqrt[7]{y}\) Solution
  2. \(\sqrt[3]{{{x^2}}}\) Solution
  3. \(\sqrt[6]{{ab}}\) Solution
  4. \(\sqrt {{w^2}{v^3}} \) Solution

For problems 5 – 7 evaluate the radical.

  1. \(\sqrt[4]{{81}}\) Solution
  2. \(\sqrt[3]{{ - 512}}\) Solution
  3. \(\sqrt[3]{{1000}}\) Solution

For problems 8 – 12 simplify each of the following. Assume that x, y and z are all positive.

  1. \(\sqrt[3]{{{x^8}}}\) Solution
  2. \(\sqrt {8{y^3}} \) Solution
  3. \(\sqrt[4]{{{x^7}{y^{20}}{z^{11}}}}\) Solution
  4. \(\sqrt[3]{{54{x^6}{y^7}{z^2}}}\) Solution
  5. \(\sqrt[4]{{4{x^3}y}}\,\,\sqrt[4]{{8{x^2}{y^3}{z^5}}}\) Solution

For problems 13 – 15 multiply each of the following. Assume that x is positive.

  1. \(\sqrt x \left( {4 - 3\sqrt x } \right)\) Solution
  2. \(\left( {2\sqrt x + 1} \right)\left( {3 - 4\sqrt x } \right)\) Solution
  3. \(\left( {\sqrt[3]{x} + 2\,\,\sqrt[3]{{{x^2}}}} \right)\left( {4 - \sqrt[3]{{{x^2}}}} \right)\) Solution

For problems 16 – 19 rationalize the denominator. Assume that x and y are both positive.

  1. \(\displaystyle \frac{6}{{\sqrt x }}\) Solution
  2. \(\displaystyle \frac{9}{{\sqrt[3]{{2x}}}}\) Solution
  3. \(\displaystyle \frac{4}{{\sqrt x + 2\sqrt y }}\) Solution
  4. \(\displaystyle \frac{{10}}{{3 - 5\sqrt x }}\) Solution