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

1. $$\sqrt{y}$$ Solution
2. $$\sqrt{{{x^2}}}$$ Solution
3. $$\sqrt{{ab}}$$ Solution
4. $$\sqrt {{w^2}{v^3}}$$ Solution

For problems 5 – 7 evaluate the radical.

1. $$\sqrt{{81}}$$ Solution
2. $$\sqrt{{ - 512}}$$ Solution
3. $$\sqrt{{1000}}$$ Solution

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

1. $$\sqrt{{{x^8}}}$$ Solution
2. $$\sqrt {8{y^3}}$$ Solution
3. $$\sqrt{{{x^7}{y^{20}}{z^{11}}}}$$ Solution
4. $$\sqrt{{54{x^6}{y^7}{z^2}}}$$ Solution
5. $$\sqrt{{4{x^3}y}}\,\,\sqrt{{8{x^2}{y^3}{z^5}}}$$ 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. $$\left( {\sqrt{x} + 2\,\,\sqrt{{{x^2}}}} \right)\left( {4 - \sqrt{{{x^2}}}} \right)$$ Solution

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

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