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This is a little bit in advance, but I wanted to let everyone know that my servers will be undergoing some maintenance on May 17 and May 18 during 8:00 AM CST until 2:00 PM CST. Hopefully the only inconvenience will be the occasional “lost/broken” connection that should be fixed by simply reloading the page. Outside of that the maintenance should (fingers crossed) be pretty much “invisible” to everyone.

Paul
May 6, 2021

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Assignment Problems Notice
Please do not email me to get solutions and/or answers to these problems. I will not give them out under any circumstances nor will I respond to any requests to do so. The intent of these problems is for instructors to use them for assignments and having solutions/answers easily available defeats that purpose.

For problems 1 – 6 write the expression in exponential form.

1. $$\sqrt {3n}$$
2. $$\sqrt[6]{{2y}}$$
3. $$\sqrt[5]{{7{x^3}}}$$
4. $$\sqrt[4]{{xyz}}$$
5. $$\sqrt {x + y}$$
6. $$\sqrt[3]{{{a^3} + {b^3}}}$$

For problems 7 – 12 evaluate the radical.

1. $$\sqrt {256}$$
2. $$\sqrt[4]{{256}}$$
3. $$\sqrt[8]{{256}}$$
4. $$\sqrt[5]{{ - 1024}}$$
5. $$\sqrt[3]{{ - 216}}$$
6. $$\sqrt[3]{{343}}$$

For problems 13 – 22 simplify each of the following. Assume that $$x$$, $$y$$ and $$z$$ are all positive.

1. $$\sqrt {{z^5}}$$
2. $$\sqrt[3]{{{z^5}}}$$
3. $$\sqrt[3]{{16{x^{17}}}}$$
4. $$\sqrt[6]{{128{y^{11}}}}$$
5. $$\sqrt {{x^3}{y^{17}}{z^4}}$$
6. $$\sqrt[4]{{{x^3}{y^{20}}{z^5}}}$$
7. $$\sqrt[4]{{729{x^7}y\,{z^{13}}}}$$
8. $$\sqrt[3]{{4{x^2}y}}\,\,\,\sqrt[3]{{10{x^5}{y^2}}}$$
9. $$\sqrt {3x} \,\,\sqrt {6x} \,\,\sqrt {14x}$$
10. $$\sqrt[4]{{2x{y^3}}}\,\,\,\sqrt[4]{{32{x^2}{y^2}}}$$

For problems 23 – 26 multiply each of the following. Assume that $$x$$ is positive.

1. $$\left( {2\sqrt x + 4} \right)\left( {\sqrt x - 7} \right)$$
2. $$\sqrt[3]{x}\left( {\sqrt[3]{x} + 2\sqrt[3]{{{x^4}}}} \right)$$
3. $$\left( {\sqrt x + \sqrt {2y} } \right)\left( {\sqrt x - \sqrt {2y} } \right)$$
4. $${\left( {\sqrt[4]{x} + \sqrt[4]{{{x^2}}}} \right)^2}$$

For problems 27 – 35 rationalize the denominator. Assume that $$x$$ and $$y$$ are both positive.

1. $$\displaystyle \frac{9}{{\sqrt y }}$$
2. $$\displaystyle \frac{3}{{\sqrt {7x} }}$$
3. $$\displaystyle \frac{1}{{\sqrt[4]{x}}}$$
4. $$\displaystyle \frac{{12}}{{\sqrt[5]{{3{x^2}}}}}$$
5. $$\displaystyle \frac{2}{{4 - \sqrt x }}$$
6. $$\displaystyle \frac{9}{{\sqrt {3y} + 2}}$$
7. $$\displaystyle \frac{4}{{\sqrt 7 - 6\sqrt x }}$$
8. $$\displaystyle \frac{{ - 6}}{{\sqrt {5x} + 10\sqrt y }}$$
9. $$\displaystyle \frac{{4 + x}}{{x - \sqrt x }}$$

For problems 36 – 38 determine if the statement is true or false. If it is false explain why it is false.

1. $$3{x^{\frac{1}{2}}} = \sqrt {3x}$$
2. $$\sqrt[3]{{x + 6}} = \sqrt[3]{x} + \sqrt[3]{6}$$
3. $$\sqrt[4]{{{x^2}}} = \sqrt x$$
4. For problems 13 – 35 above we always added the instruction to assume that the variables were positive. Why was this instruction added? How would the answers to the problems change if we did not have that instruction?