91Ó°ÊÓ

Perform the indicated operations. $$\frac{\sqrt{27}}{2}+\frac{\sqrt{75}}{7}$$

In Exercises \(65-74,\) simplify each radical expression and then rationalize the denominator. $$-\sqrt{\frac{150 a^{3}}{b^{5}}}$$

In Exercises \(63-84,\) divide and simplify to the form \(a+b i\) $$\frac{9}{1-2 i}$$

Multiply and simplify. Assume that all variables in a radicand represent positive real numbers and no radicands involve negative quantities raised to even powers. $$\sqrt{5 x y} \cdot \sqrt{10 x y^{2}}$$

Use a graphing utility to solve each radical equation. Graph each side of the equation in the given viewing rectangle. The equation's solution set is given by the \(x\) -coordinate(s) of the point (s) of intersection. Check by substitution. $$\begin{aligned} &\sqrt{2 x+2}=\sqrt{3 x-5}\\\ &[-1,10,1] \text { by }|-1,5,1| \end{aligned}$$

In Exercises \(65-74,\) simplify each radical expression and then rationalize the denominator. $$\sqrt{\frac{7 m^{2} n^{3}}{14 m^{3} n^{2}}}$$

Use a graphing utility to solve each radical equation. Graph each side of the equation in the given viewing rectangle. The equation's solution set is given by the \(x\) -coordinate(s) of the point (s) of intersection. Check by substitution. $$\begin{aligned} &\sqrt{x}+3=5\\\ &[-1,6,1] \text { by }[-1,6,1] \end{aligned}$$

Multiply and simplify. Assume that all variables in a radicand represent positive real numbers and no radicands involve negative quantities raised to even powers. $$2 \sqrt{5} \cdot 3 \sqrt{40}$$

In Exercises \(55-78,\) use properties of rational exponents to simplify each expression. Assume that all variables represent positive numbers. $$\left(2 x^{\frac{1}{5}}\right)^{5}$$

Perform the indicated operations. $$3 x \sqrt{8 x y^{2}}-5 y \sqrt{32 x^{3}}+\sqrt{18 x^{3} y^{2}}$$