How to Multiply Radical Expressions? (+FREE Worksheet!)

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.

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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, simplify:

\(2\sqrt{5}×\sqrt{3}=(2×1)×(\sqrt{5}×\sqrt{3})=(2)(\sqrt {15)}=2\sqrt{15}\)

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 outside of the radicals and the radical parts. Then, simplify:

\(4\sqrt{3}×3\sqrt{2}=\) \((4×3) × (\sqrt{3} × \sqrt{2)}\)\(=(12) (\sqrt{6)} = 12\sqrt{6}\)

Exercises for Multiplying Radical Expressions

Multiply 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. \(\color{blue}{2\sqrt{10}}\)
3. \(\color{blue}{6\sqrt{6}}\)
4. \(\color{blue}{18\sqrt{14}}\)
5. \(\color{blue}{30x}\)
6. \(\color{blue}{-49\sqrt{6}}\)