Multiply two square-root terms and simplify the product
a =
b =
c =
d =
Result
Simplified Product
Step-by-Step Derivation
Radical Multiplication Formula
a√b × c√d = ac√(bd)
Radical multiplication combines the outside coefficients and multiplies the radicands under one square root. For nonnegative radicands, √b × √d = √(bd), then the product is simplified by extracting perfect-square factors.
⚠Note: This tool assumes real square roots with nonnegative integer radicands. It simplifies the final radical product but does not handle complex-number radical multiplication.
How Radical Multiplication Works
Multiply the outside numbers first, multiply the radicands second, then simplify the resulting square root. The first product may be correct but not fully simplified, so the final step checks for perfect-square factors.
Multiply Coefficients
The outside numbers multiply to form the new coefficient.
Multiply Radicands
The values under the square roots multiply together.
Simplify Product
Perfect-square factors move outside the radical.
Exact Result
The final answer stays exact instead of using rounded decimals.
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