Formulas & tables/Mathematics/Powers and roots/Root of a product
Root of a product

Root of a product

abn=an bn\sqrt[n]{ab}=\sqrt[n]{a}\,\sqrt[n]{b}

Result unit: — (liczba)

What it describes

The root of a product equals the product of the roots of its factors.

Symbols

a,ba, b
non-negative numbers
nn
index of the root

Where it comes from

The root of a product can be split into a product of roots — useful for taking a factor outside the radical.

When to use it

Simplifying roots (e.g. 12=23\sqrt{12}=2\sqrt3).

Example

Simplify 4⋅9\sqrt{4\cdot9}.
Substitution4⋅9\sqrt4\cdot\sqrt9.
Result2⋅3=62\cdot3=6.

Related formulas

Root as a fractional power Power of a product

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