Multiplying Radicals Calculator

Multiply radical expressions and see the simplified radical form beside the computed decimal value.

Last updated: March 2026 | By ForgeCalc Engineering

Radical Product Solver

Square root product rule

Coefficient 1

Radicand 1

Coefficient 2

Radicand 2

Radical Steps

1.Multiply the coefficients: 2 × 4 = 8

2.Multiply the radicands: √3 × √5 = √15

3.Combine: 8√15

4.Radical is already simplified.

Simplified Result

8√15

Decimal: 30.9839

When multiplying radicals, multiply the coefficients together and multiply the numbers under the radical sign. Then simplify the result if possible.

a√b × c√d = (a × c)√(b × d)

Example: 2√3 × 4√5 = 8√15.

2 × 4 = 8, and √3 × √5 = √15

Can I multiply radicals with different indices?

This calculator is built for square roots, so the product rule is applied in that context.

What if a radicand is negative?

Negative radicands are rejected because square roots of negative numbers are not real.

Does it simplify the result?

Yes. If a perfect square factor is present, the radical is simplified.

Can the coefficient be a decimal?

Yes. Any finite real coefficient is accepted.

Related Tools

Find cube roots.

Divide exponential expressions.

Divide radical expressions.

Calculate powers.

Convert to exponential form.

Multiply exponential expressions.