Multiplying radicals with variables

Multiplying radicals with variables

By Yessenia Rivera

Reminder: How to simplify a radical

Multiplying Radicals

• When multiplying radicals with the same variables follow the following steps:

• Step 1: Multiply the same variables together. *Remember when you multiply the same variables you add the exponents

• Step 2: Simplify if possible ​

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Multiple Choice

Multiply and simplify if possible:

$$\sqrt[]{x^2}\cdot\sqrt[]{x^8}$$  

• $$x^5$$  

• $$x^3\sqrt[]{x}$$  

• $$x^{10}$$  

• $$x^4$$  

Multiple Choice

Multiply and simplify if possible:

$$\sqrt[]{x^4}\cdot\sqrt[]{x^5}$$  

• $$\sqrt[]{x^{20}}$$  

• $$\sqrt[]{x}$$  

• $$x^9$$  

• $$x^4\sqrt[]{x}$$  

Multiple Choice

Multiply and simplify if possible:

$$\sqrt[]{x^8}\cdot\sqrt[]{x^5}$$  

• $$x^4$$  

• $$x^6\sqrt[]{x}$$  

• $$\sqrt[]{x^{40}}$$  

• $$\sqrt[]{x^3}$$  

Multiplying radicals with multiple variables inside

• When multiplying radicals with multiple variables follow the following steps:

• Step 1: Multiply the same variables together (x with x, y with y, etc). *Remember when you multiply the same variables you add the exponents

• Step 2: Simplify if possible ​

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​Example

Subject | Subject

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Multiple Choice

Multiply and simplify if possible:

$$\sqrt[]{x^4y^2}\cdot\sqrt[]{x^7y^5}$$  

• $$x^3y\sqrt[]{xy}$$  

• $$x^{11}y^7$$  

• $$x^5y^3\sqrt[]{xy}$$  

• $$x^3y^2$$  

Multiple Choice

Multiply and simplify if possible:

$$\sqrt[]{x^8y^2}\cdot\sqrt[]{x^6y^8}$$  

• $$x^{14}y^{10}$$  

• $$x^7y^5$$  

• $$x^7y^5\sqrt[]{xy}$$  

• $$x^{14}y^{10}\sqrt[]{y}$$  

Multiple Choice

Multiply and simplify if possible:

$$\sqrt[]{xy^3z^8}\cdot\sqrt[]{x^7y^4z}$$  

• $$x^4y^3z^4\sqrt[]{yz}$$  

• $$x^8y^7z^9$$  

• $$x^6y^3\sqrt[]{xyz}$$  

• $$xyz^{24}$$  

Multiplying Radicals

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​Multiply numbers together

​Multiply variables together

​Check if you can simplify

​Simplify

Multiple Choice

Multiply and simplify if possible:

$$\sqrt[]{4x^2}\cdot\sqrt[]{6x^6}$$  

• $$\sqrt[]{10x^{10}}$$  

• $$2x^4\sqrt[]{6}$$  

• $$24x^8$$  

• $$x^4\sqrt[]{2}$$  

Multiple Choice

Multiply and simplify if possible:

$$\sqrt[]{5x^{ }}\cdot\sqrt[]{10x^5}$$  

• $$\sqrt[]{15x^6}$$  

• $$\sqrt[]{5x^4}$$  

• $$5x^6\sqrt[]{2}$$  

• $$5x^3\sqrt[]{2}$$  

Multiple Choice

Multiply and simplify if possible:

$$\sqrt[]{4x^7}\cdot\sqrt[]{6x^2}$$  

• $$4x^3\sqrt[]{5x^2}$$  

• $$2x^4\sqrt[]{6x}$$  

• $$6\sqrt[]{4x^9}$$  

• $$2x\sqrt[]{6}$$  

Poll

How well did you understand the lesson?

• Very well

• Need more practice

• I don't understand