Chapter 9

Simplify each expression by performing the indicated operation. $$ (3+\sqrt{3})(3-\sqrt{3}) $$

For the following problems, simplify the expressions. $$ -2 \sqrt{9 x^{2}-42 x+49}+5 \sqrt{18 x^{2}-84 x+98} $$

For the following problems, simplify each of the radical expressions. $$ \sqrt{\frac{3}{10}} $$

Find each of the following products. $$ \sqrt{x^{6}} \sqrt{x^{2}} \sqrt{x^{9}} $$

For the following problems, simplify each expressions. $$ \frac{-6}{\sqrt{5}-1} $$

For the following problems, write the proper restrictions that must be placed on the variable so that the expression represents a real number. $$ \sqrt{7 x+8} $$

For the following problems, simplify the expressions. $$ -10 \sqrt{56 a^{3} b^{7}}+2 a^{2} b \sqrt{126 a b^{5}} $$

Simplify each expression by performing the indicated operation. $$ (2+\sqrt{5})(2-\sqrt{5}) $$

For the following problems, simplify each of the radical expressions. $$ \sqrt{\frac{4}{3}} $$

Find each of the following products. $$ \sqrt{2 a^{4}} \sqrt{5 a^{3}} \sqrt{2 a^{7}} $$

For the following problems, simplify each expressions. $$ \frac{-6}{\sqrt{7}+2} $$

For the following problems, write the proper restrictions that must be placed on the variable so that the expression represents a real number. $$ \sqrt{-2 x-8} $$

For the following problems, simplify the expressions. $$ \frac{\sqrt{3 x}-\sqrt{5 x}}{\sqrt{7 x}+\sqrt{2 x}} $$

Simplify each expression by performing the indicated operation. $$ (8+\sqrt{10})(8-\sqrt{10}) $$

For the following problems, simplify each of the radical expressions. $$ -\sqrt{\frac{2}{5}} $$

Find each of the following products. $$ \sqrt{x^{n}} \sqrt{x^{n}} $$

For the following problems, simplify each expressions. $$ \frac{3}{\sqrt{3}-\sqrt{2}} $$

For the following problems, write the proper restrictions that must be placed on the variable so that the expression represents a real number. $$ \sqrt{-5 y+15} $$

For the following problems, simplify the expressions. $$ \frac{\sqrt{6 a}+\sqrt{2 a}}{\sqrt{3 a}-\sqrt{5 a}} $$

Simplify each expression by performing the indicated operation. $$ (6+\sqrt{7})(6-\sqrt{7}) $$

For the following problems, simplify each of the radical expressions. $$ -\sqrt{\frac{3}{10}} $$

For the following problems, simplify each expression by removing the radical sign. $$ \sqrt{m^{6}} $$

Find each of the following products. $$ \sqrt{y^{2} n} \sqrt{y^{4} n} $$

For the following problems, solve the equations. $$ \sqrt{3 x}=9 $$

Simplify each expression by performing the indicated operation. $$ (\sqrt{2}+\sqrt{3})(\sqrt{2}-\sqrt{3}) $$

For the following problems, simplify each of the radical expressions. $$ \sqrt{\frac{16 a^{2}}{5}} $$

For the following problems, simplify each expressions. $$ \frac{\sqrt{5}}{\sqrt{8}-\sqrt{6}} $$

Find each of the following products. $$ \sqrt{a^{2 n+5}} \sqrt{a^{3}} $$

For the following problems, solve the equations. $$ \sqrt{4 a}=16 $$

Simplify each expression by performing the indicated operation. $$ (\sqrt{5}+\sqrt{2})(\sqrt{5}-\sqrt{2}) $$

For the following problems, simplify each of the radical expressions. $$ \sqrt{\frac{24 a^{5}}{7}} $$

For the following problems, simplify each expressions. $$ \frac{\sqrt{12}}{\sqrt{12}-\sqrt{8}} $$

Find each of the following products. $$ \sqrt{2 m^{3 n+1}} \sqrt{10 m^{n+3}} $$

For the following problems, solve the equations. $$ \sqrt{x}+7=4 $$

Simplify each expression by performing the indicated operation. $$ (\sqrt{a}+\sqrt{b})(\sqrt{a}-\sqrt{b}) $$

For the following problems, simplify each of the radical expressions. $$ \sqrt{\frac{72 x^{2} y^{3}}{5}} $$

For the following problems, simplify each expression by removing the radical sign. $$ \sqrt{h^{16}} $$

Find each of the following products. $$ \sqrt{75(a-2)^{7}} \sqrt{48 a-96} $$

Simplify each expression by performing the indicated operation. $$ (\sqrt{x}+\sqrt{y})(\sqrt{x}-\sqrt{y}) $$

For the following problems, simplify each of the radical expressions. $$ \sqrt{\frac{2}{a}} $$

For the following problems, simplify each expression by removing the radical sign. $$ \sqrt{x^{4} y^{10}} $$

Find each of the following products. $$ \sqrt{2}(\sqrt{8}+\sqrt{6}) $$

For the following problems, solve the equations. $$ \sqrt{4 a+5}=21 $$

For the following problems, simplify each of the radical expressions. $$ \sqrt{\frac{5}{b}} $$

For the following problems, simplify each expressions. $$ \frac{\sqrt{2}}{\sqrt{3}-\sqrt{2}} $$

Find each of the following products. $$ \sqrt{5}(\sqrt{3}+\sqrt{7}) $$

For the following problems, solve the equations. $$ \sqrt{3 m+7}=10 $$

Simplify each expression by performing the indicated operation. $$ \frac{4}{6+\sqrt{2}} $$

For the following problems, simplify each of the radical expressions. $$ \sqrt{\frac{6}{x^{3}}} $$

For the following problems, simplify each expressions. $$ \frac{\sqrt{a}}{\sqrt{a}+\sqrt{b}} $$