Math Applications with Radical Expressions

Multiplying radicals with variables

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​Dr. Tom Giles

​Quick Review of Addition & Subtraction

Radical Rules

Always keep your cheat sheet near by!

Make sure you show all of your work (PRIME Factor Tree) in your math notebook.

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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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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​Multiply numbers together

​Multiply variables together

​Check if you can simplify

​Simplify

Multiplying Radicals

When only radicands

​​1. Combine and multiply​

​​2. Check factors and simplify​

When simplifying is possible

Sometimes, multiplying the radicals can result in expressions that can still be simplified.​

If the radicals have coefficients, do the work in two parts:

1. Multiply​ the coefficients.

2. Multiply the radicals.

3. Don't forget to check if you can simplify.​

When there are coefficients

Multiple Choice

Multiply and simplify if possible:

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

• $$x^4y^3z^4\sqrt[]{yz}$$  

• $$x^8y^7z^9$$  

• $$x^6y^3\sqrt[]{xyz}$$  

• $$xyz^{24}$$  

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:

$$\sqrt[]{x^4}\cdot\sqrt[]{x^5}$$  

• $$\sqrt[]{x^{20}}$$  

• $$\sqrt[]{x}$$  

• $$x^9$$  

• $$x^4\sqrt[]{x}$$  

Multiple Choice

Multiply and simplify if possible:

$$\sqrt[]{x^2}\cdot\sqrt[]{x^8}$$  

• $$x^5$$  

• $$x^3\sqrt[]{x}$$  

• $$x^{10}$$  

• $$x^4$$  

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 the radical expressions together.

$$\sqrt[]{7}\cdot\sqrt[]{2}$$  

• $$\sqrt[]{9}$$  

• $$3$$  

• $$\sqrt[]{14}$$  

• $$14$$  

Multiple Choice

$$2\sqrt[]{5}\left(\sqrt[]{4}+2\sqrt[]{3}\right)$$   Multiply & Simplify

• $$4\sqrt[]{5}+4\sqrt[]{15}$$  

• $$8\sqrt[]{20}$$  

• $$4\sqrt[]{5}$$  

• $$4\sqrt[]{20}+2\sqrt[]{15}$$  

Multiple Choice

Multiply the radical expressions together.

$$5\sqrt[]{2}\cdot7\sqrt[]{3}$$  

•   $$12\sqrt[]{5}$$  

•   $$10\sqrt[]{21}$$  

•   $$35\sqrt[]{6}$$  

•   $$35\sqrt[]{5}$$  

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