Honors Algebra 2: Extra Practice on Solving Radical Equations

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Solve the following over the real numbers:

  1. \( \displaystyle \sqrt[3]{3y^{-1}} = -6\)
    2. Solution

    \( \displaystyle y = -\frac{1}{72} \)

  2. \( \displaystyle 4 - \sqrt{10 - 3a} = a\)
    3. Solution

    \( \displaystyle a = \{ 2, 3 \} \)

  3. \( \displaystyle 3\sqrt{2n + 3} = 2n + 5\)
    4. Solution

    \( \displaystyle n = \left\{ -1, \frac{1}{2} \right\} \)

  4. \( \displaystyle \sqrt{x^{2} + x - 3} = 3\)
    5. Solution

    \( \displaystyle x = \{-4, 3 \} \)

  5. \( \displaystyle \sqrt[3]{y^{2} - 12y} = 4\)
    6. Solution

    \( \displaystyle y = \{ -4, 16 \} \)

  6. \( \displaystyle \sqrt[4]{5x^{2} + 3} = 2 \sqrt[4]{x}\)
    7. Solution

    \( \displaystyle x = \left\{ \frac{1}{5}, 3 \right\} \)

  7. \( \displaystyle \sqrt {\frac{x - 3}{x + 2}} = \frac{2}{3}\)
    8. Solution

    \( \displaystyle x = 7 \)

  8. \( \displaystyle \sqrt{\frac{2}{y + 3}} = \sqrt{\frac{3}{2y + 2}}\)
    9. Solution

    \( \displaystyle y = 5 \)

  9. \( \displaystyle \sqrt{\frac{x - 2}{x - 2}} = \frac{x - 4}{\sqrt{x - 2}}\)
    10. Solution

    \( \displaystyle x = 6 \)

  10. \( \displaystyle \sqrt{y + 15} - \sqrt{2y + 7} = 1\)
    11. Solution

    \( \displaystyle y = 1 \)

  11. \( \displaystyle \sqrt{3x - 5} + \sqrt{x - 1} = 2\)
    12. Solution

    \( \displaystyle x = 2 \)

  12. \( \displaystyle \sqrt{3x + 9} - \sqrt{2x + 7} = 1\)
    13. Solution

    \( \displaystyle y = 9 \)