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.

## Related Topics

- How to Rationalize Radical Expressions
- How to Solve Radical Equations
- How to Simplify Radical Expressions
- How to Rationalize Radical Expressions
- How to Find Domain and Range of Radical Functions

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

To multiply 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

### Multiply Radical Expressions.

- \(\color{blue}{\sqrt{2}×\sqrt{6}=}\)
- \(\color{blue}{\sqrt{5}×\sqrt{8}=}\)
- \(\color{blue}{\sqrt{8}×3\sqrt{3}=}\)
- \(\color{blue}{3\sqrt{7}×6\sqrt{2}=}\)
- \(\color{blue}{\sqrt{6x}×5\sqrt{6x}=}\)
- \(\color{blue}{-7\sqrt{2}×7\sqrt{3}=}\)

- \(\color{blue}{2\sqrt{3}}\)
- \(\color{blue}{\sqrt{40}=2\sqrt{10}}\)
- \(\color{blue}{3\sqrt{24}}\)
- \(\color{blue}{18\sqrt{14}}\)
- \(\color{blue}{30x}\)
- \(\color{blue}{-49\sqrt{6}}\)