Multiplying and Dividing Radicals Algebra

​9.1 D4 Multiply Radicals

​Learning Target

​SWBAT multiply radicals by using the product rules of radicals

Multiple Choice

Simplify: $$\sqrt{162}$$

• 8√2
• 12√3
• 9√2
• 6√3

Multiple Choice

Simplify: $$3\sqrt{7}+9\sqrt{7}$$

• 6√7
• 21√7
• 15√7
• 12√7

Multiple Choice

Simplify: $$5\sqrt{3}-\sqrt{3}$$

• $$4\sqrt{3}$$

• $$-4\sqrt{3}$$

• $$3\sqrt{4}$$

• $$-3\sqrt{4}$$

Multiple Choice

Simplify: $$3\sqrt{75}+2\sqrt{3}$$

• $$3\sqrt{17}$$

• $$-3\sqrt{17}$$

• $$17\sqrt{3}$$

• $$-17\sqrt{3}$$

Multiple Choice

Simplify: $$\sqrt{12}+2\sqrt{3}-5\sqrt{3}$$

• $$3\sqrt{17}$$

• $$-3\sqrt{3}$$

• $$3\sqrt{3}$$

• $$-\sqrt{3}$$

Multiple Choice

Simplify: $$2\left(x+5\right)$$

• $$2x+10$$

• $$-2x+10$$

• $$10x+2$$

• $$-10x+2$$

Multiple Choice

Simplify: $$m\left(m-8\right)$$

• $$m^2-8m$$

• $$8m^2+m$$

• $$8m^2-m$$

• $$m^2+8m$$

Multiple Choice

Simplify: $$\left(x-3\right)\left(x+3\right)$$

• $$x^2-9$$

• $$x^2+9$$

• $$x^2$$

• $$x^2-9x$$

​Multiplying Radicals

​Example 1: Multiply Radicals

Multiple Choice

$$-8\sqrt{15}\cdot2\sqrt{10}$$

• $$-8\sqrt{150}$$

• $$-4\sqrt{150}$$

• $$-80\sqrt{6}$$

• $$-6\sqrt{80}$$

​Example 2: Multiply Radicals

Multiple Choice

$$2\sqrt{3}\left(3\sqrt{5}+7\sqrt{2}\right)$$

• $$6+2\sqrt{15}$$

• $$2+4\sqrt{15}$$

• $$6\sqrt{15}+14\sqrt{6}$$

• $$4+4\sqrt{5}$$

​Example 3: Multiply Radicals

Multiple Choice

$$\left(\sqrt{8}+\sqrt{6}\right)\left(\sqrt{2}+\sqrt{10}\right)$$

• $$4+2\sqrt{15}+2\sqrt{3}+12$$

• $$4+2\sqrt{15}+2\sqrt{3}+6$$

• $$4+2\sqrt{15}+2\sqrt{3}+8$$

• $$4+4\sqrt{5}+2\sqrt{3}+2\sqrt{15}$$

​Example 4: Multiply Radicals

Multiple Choice

$$\left(\sqrt{5}-3\right)^2$$

• $$14+6\sqrt{5}$$

• $$14-6\sqrt{3}$$

• $$14+5\sqrt{3}$$

• $$14-6\sqrt{5}$$

Multiple Choice

$$\sqrt{5}\left(\sqrt{2}+\sqrt{5}\right)$$

• $$6\sqrt{5}$$

• $$-6\sqrt{3}$$

• $$5\sqrt{3}$$

• $$5\sqrt{10}$$