9.10: Proficiency Exam
Proficiency Exam
For the following problems, simplify each of the square root expressions.
\(\sqrt{8} \cdot \sqrt{5}\)
- Answer
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\(2 \sqrt{10}\)
\(\dfrac{\sqrt{80}}{\sqrt{12}}\)
- Answer
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\(\dfrac{2 \sqrt{15}}{3}\)
\(\dfrac{\sqrt{n^2 + n - 12}}{\sqrt{n-3}}\)
- Answer
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\(\sqrt{n + 4}\)
\(\sqrt{24a^3b^5c^8}\)
- Answer
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\(2ab^2c^4 \sqrt{6ab}\)
\(\sqrt{\dfrac{64x^4y^5z^6}{49a^3b^2c^9}}\)
- Answer
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\(\dfrac{8x^2y^2z^3\sqrt{acy}}{7a^2bc^5}\)
\(\sqrt{(x-2)^2(x+1)^4}\)
- Answer
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\((x-2)(x+1)^2\)
\(\sqrt{a^2-8a+16}\)
- Answer
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\(a-4\)
\(\dfrac{4}{2 + \sqrt{x}}\)
- Answer
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\(\dfrac{8 - 4\sqrt{x}}{4 - x}\)
\(\dfrac{\sqrt{3a}}{\sqrt{2a} + \sqrt{5a}}\)
- Answer
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\(\dfrac{\sqrt{15} - \sqrt{6}}{3}\)
\(2x\sqrt{27} + x\sqrt{12}\)
- Answer
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\(8x\sqrt{3}\)
\(-3a\sqrt{a^5b^3} + 2a^3b\sqrt{ab}\)
- Answer
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\(-a^3b\sqrt{ab}\)
\(\sqrt{10}(\sqrt{8} - \sqrt{2})\)
- Answer
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\(2\sqrt{5}\)
\((3 + \sqrt{6})(2 + \sqrt{5})\)
- Answer
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\(6 + 3\sqrt{5} + 2\sqrt{6} + \sqrt{30}\)
\((\sqrt{10} - \sqrt{3})(\sqrt{5} + \sqrt{2})\)
- Answer
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\(5\sqrt{2} + 2\sqrt{5} - \sqrt{15} - \sqrt{6}\)
\((4 - \sqrt{5y})^2\)
- Answer
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\(16 - 8\sqrt{5y} + 5y\)
\(\dfrac{6 - \sqrt{3}}{4 + \sqrt{2}}\)
- Answer
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\(\dfrac{24 - 6\sqrt{2} - 4\sqrt{3} + \sqrt{6}}{14}\)
\(\dfrac{\sqrt{2} + \sqrt{3}}{\sqrt{3} - \sqrt{5}}\)
- Answer
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\(-\dfrac{3 + \sqrt{6} + \sqrt{10} + \sqrt{15}}{2}\)
For the following problems, solve the equations.
\(\sqrt{x + 8} = 4\)
- Answer
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\(x = 8\)
\(\sqrt{3a + 1} = 4\)
- Answer
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\(a = 5\)
\(\sqrt{2x} = -3\)
- Answer
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No Solution
\(\sqrt{3x + 18} + 7 = 0\)
- Answer
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No real solution
\(\sqrt{3m - 5} = \sqrt{2m + 1}\)
- Answer
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\(m = 6\)
\(2\sqrt{a + 2} - 2= 0\)
- Answer
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\(a = -1\)
\(\sqrt{b - 7} - \sqrt{5b + 1} = 0\)
- Answer
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No Solution
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
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a) \(S = 217\)
b) \(E = 52\)