# How to Multiply Radical Expressions

A radical expression is an expression containing a square root and to multiply these expressions, you have to go through step by step, which in this blog post you will learn how to do with examples.

## A step-by-step guide to Multiplying Radical Expressions

• Multiply the numbers and expressions outside of the radicals.
• Multiply the numbers and expressions inside the radicals.
• Simplify if needed.

## Examples

### Multiplying Radical Expressions – Example 1:

Evaluate. $$2\sqrt{5}×\sqrt{3}$$

Solution:

Multiply the numbers outside of the radicals and the radical parts. Then: $$2\sqrt{5}×\sqrt{3}=2×1×\sqrt{5}×\sqrt{3}=2\sqrt{15}$$

### Multiplying Radical Expressions – Example 2:

Simplify. $$3x\sqrt{3}×4\sqrt{x}$$

Solution:

Multiply the numbers outside of the radicals and the radical parts. Then, simplify: $$3x\sqrt{3}×4\sqrt{x}=(3x×4)×(\sqrt{3}×\sqrt{x})=(12x)(\sqrt{3x})=12x\sqrt{3x}$$

### Multiplying Radical Expressions – Example 3:

Evaluate. $$\sqrt{36}×\sqrt{4}$$

Solution:

The first factor the numbers: $$36=6^2$$ and $$4=2^2$$
Then: $$\sqrt{36}×\sqrt{4}=\sqrt{6^2}×\sqrt{2^2}$$
Now use radical rule: $$\sqrt[n]{a^n}=a$$, Then: $$\sqrt{6^2}×\sqrt{2^2}=6×2=12$$

### Multiplying Radical Expressions – Example 4:

Evaluate. $$4\sqrt{3}×3\sqrt{2}=$$

Solution:

Multiply the numbers: $$4×3=12$$
$$4\sqrt{3}×3\sqrt{2}=12\sqrt{3} \sqrt{2}$$
Use radical rule: $$\sqrt{a} \sqrt{b}=\sqrt{ab}→12\sqrt{3} \sqrt{2}=12\sqrt{3×2}=12\sqrt{6}$$

## Exercises for Multiplying Radical Expressions

1. $$\color{blue}{\sqrt{2}×\sqrt{6}=}$$
2. $$\color{blue}{\sqrt{5}×\sqrt{8}=}$$
3. $$\color{blue}{\sqrt{8}×3\sqrt{3}=}$$
4. $$\color{blue}{3\sqrt{7}×6\sqrt{2}=}$$
5. $$\color{blue}{\sqrt{6x}×5\sqrt{6x}=}$$
6. $$\color{blue}{-7\sqrt{2}×7\sqrt{3}=}$$
1. $$\color{blue}{2\sqrt{3}}$$
2. $$\color{blue}{\sqrt{40}=2\sqrt{10}}$$
3. $$\color{blue}{3\sqrt{24}}$$
4. $$\color{blue}{18\sqrt{14}}$$
5. $$\color{blue}{30x}$$
6. $$\color{blue}{-49\sqrt{6}}$$

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