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9.10: Proficiency Exam

  • Page ID
    60065
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    Proficiency Exam

    For the following problems, simplify each of the square root expressions.

    Exercise \(\PageIndex{1}\)

    \(\sqrt{8} \cdot \sqrt{5}\)

    Answer

    \(2 \sqrt{10}\)

    Exercise \(\PageIndex{2}\)

    \(\dfrac{\sqrt{80}}{\sqrt{12}}\)

    Answer

    \(\dfrac{2 \sqrt{15}}{3}\)

    Exercise \(\PageIndex{3}\)

    \(\dfrac{\sqrt{n^2 + n - 12}}{\sqrt{n-3}}\)

    Answer

    \(\sqrt{n + 4}\)

    Exercise \(\PageIndex{4}\)

    \(\sqrt{24a^3b^5c^8}\)

    Answer

    \(2ab^2c^4 \sqrt{6ab}\)

    Exercise \(\PageIndex{5}\)

    \(\sqrt{\dfrac{64x^4y^5z^6}{49a^3b^2c^9}}\)

    Answer

    \(\dfrac{8x^2y^2z^3\sqrt{acy}}{7a^2bc^5}\)

    Exercise \(\PageIndex{6}\)

    \(\sqrt{(x-2)^2(x+1)^4}\)

    Answer

    \((x-2)(x+1)^2\)

    Exercise \(\PageIndex{7}\)

    \(\sqrt{a^2-8a+16}\)

    Answer

    \(a-4\)

    Exercise \(\PageIndex{8}\)

    \(\dfrac{4}{2 + \sqrt{x}}\)

    Answer

    \(\dfrac{8 - 4\sqrt{x}}{4 - x}\)

    Exercise \(\PageIndex{9}\)

    \(\dfrac{\sqrt{3a}}{\sqrt{2a} + \sqrt{5a}}\)

    Answer

    \(\dfrac{\sqrt{15} - \sqrt{6}}{3}\)

    Exercise \(\PageIndex{10}\)

    \(2x\sqrt{27} + x\sqrt{12}\)

    Answer

    \(8x\sqrt{3}\)

    Exercise \(\PageIndex{11}\)

    \(-3a\sqrt{a^5b^3} + 2a^3b\sqrt{ab}\)

    Answer

    \(-a^3b\sqrt{ab}\)

    Exercise \(\PageIndex{12}\)

    \(\sqrt{10}(\sqrt{8} - \sqrt{2})\)

    Answer

    \(2\sqrt{5}\)

    Exercise \(\PageIndex{13}\)

    \((3 + \sqrt{6})(2 + \sqrt{5})\)

    Answer

    \(6 + 3\sqrt{5} + 2\sqrt{6} + \sqrt{30}\)

    Exercise \(\PageIndex{14}\)

    \((\sqrt{10} - \sqrt{3})(\sqrt{5} + \sqrt{2})\)

    Answer

    \(5\sqrt{2} + 2\sqrt{5} - \sqrt{15} - \sqrt{6}\)

    Exercise \(\PageIndex{15}\)

    \((4 - \sqrt{5y})^2\)

    Answer

    \(16 - 8\sqrt{5y} + 5y\)

    Exercise \(\PageIndex{16}\)

    \(\dfrac{6 - \sqrt{3}}{4 + \sqrt{2}}\)

    Answer

    \(\dfrac{24 - 6\sqrt{2} - 4\sqrt{3} + \sqrt{6}}{14}\)

    Exercise \(\PageIndex{17}\)

    \(\dfrac{\sqrt{2} + \sqrt{3}}{\sqrt{3} - \sqrt{5}}\)

    Answer

    \(-\dfrac{3 + \sqrt{6} + \sqrt{10} + \sqrt{15}}{2}\)

    For the following problems, solve the equations.

    Exercise \(\PageIndex{18}\)

    \(\sqrt{x + 8} = 4\)

    Answer

    \(x = 8\)

    Exercise \(\PageIndex{19}\)

    \(\sqrt{3a + 1} = 4\)

    Answer

    \(a = 5\)

    Exercise \(\PageIndex{20}\)

    \(\sqrt{2x} = -3\)

    Answer

    No Solution

    Exercise \(\PageIndex{21}\)

    \(\sqrt{3x + 18} + 7 = 0\)

    Answer

    No real solution

    Exercise \(\PageIndex{22}\)

    \(\sqrt{3m - 5} = \sqrt{2m + 1}\)

    Answer

    \(m = 6\)

    Exercise \(\PageIndex{23}\)

    \(2\sqrt{a + 2} - 2= 0\)

    Answer

    \(a = -1\)

    Exercise \(\PageIndex{24}\)

    \(\sqrt{b - 7} - \sqrt{5b + 1} = 0\)

    Answer

    No Solution

    Exercise \(\PageIndex{25}\)

    At a small business, the number of monthly sales \(S\) is approximately related to the number of employees \(E\) by \(S = 175 + 7\sqrt{E - 3}\)

    a) Determine the approximate number of sales if the number of employees is \(39\)

    b) Determine the approximate number of employees if the number of sales in \(224\)

    Answer

    a) \(S = 217\)

    b) \(E = 52\)


    This page titled 9.10: Proficiency Exam is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Denny Burzynski & Wade Ellis, Jr. (OpenStax CNX) .

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