Problems

1. Simplify each expression.

   Assume that the variables represent any real numbers.

   (a) $\sqrt{x^{24}}$

   (b) $\sqrt{y^{10}}$

2. Simplify.

   (a). $\sqrt[3]{\dfrac{216}{343}}$

   (b). $\sqrt[4]{\dfrac{16}{625}}$

   (c). $\sqrt[3]{\dfrac{1}{27}}$

3. Simplify.

   Assume that the variables represent positive real numbers.

   (a) $\sqrt[3]{64v^{21}}$

   (b) $\sqrt[4]{81y^{24}}$

   (c) $\sqrt[5]{243x^{5}}$

4. Simplify as much as possible.

   Assume that the variables represent any real numbers.

   (a). $\sqrt[7]{(2+4u)^7}$

   (b). $\sqrt[4]{y^4}$

   (c). $\sqrt[5]{(4x-8)^5}$

   (d). $\sqrt[6]{(5w+1)^6}$

5. Find the domains of the following functions. Write your answer using interval notation.

   (a). $f(x)=\sqrt[3]{3x+15}$

   (b). $g(x)=\sqrt[4]{2x-4}$

6. Graph the function.

   $f(x)=\sqrt{x}+6$

7. Graph the function.

   $f(x)=\sqrt[3]{x-2}$

Answer key

1. (a). $x^{12}$

   (b). $|y^5|$

2. (a) $\dfrac{6}{7}$

   (b) $\dfrac{2}{5}$

   (c) $\dfrac{1}{3}$

3. (a) $4v^7$

   (b) $3y^6$

   (c) $3x$

4. (a) $2+4u$

   (b) $|y|$

   (c) $4x-8$

   (d) $|5w+1|$

5. (a). $(-\infty, \infty)$

   (b). $[2, \infty)$

6. 

7.