Multiply Radical Expressions

Multiply radical expressions

When multiplying radical expressions, use the same rules as multiplying polynomials: multiply the coefficients and multiply the radicals. Then simplify the result as much as possible.

1) Multiply the coefficients

If there is a number in front of each radical, multiply those numbers first.

2) Multiply the radicands

Combine the expressions inside the radicals under one radical symbol when possible:

• (\sqrt{a}\cdot\sqrt{b}=\sqrt{ab})
• ((m\sqrt{a})(n\sqrt{b})=mn\sqrt{ab})

3) Simplify

Look for perfect squares inside the radical. Pull them out if possible. Also reduce any fractions if they appear.

4) Watch the signs

A negative times a positive is negative, and a negative times a negative is positive. Keep the sign of the final product.

5) Check your answer

You can verify by expanding carefully and making sure the radical is in simplest form. If your result still has a perfect square inside the radical, simplify more.

Example structure: [(2\sqrt{3})(5\sqrt{6})=10\sqrt{18}=10\sqrt{9\cdot2}=30\sqrt{2}]

A good final answer has no unnecessary factors inside the radical and no unsimplified numerical factors outside.