Simplifying Radicals with Negative Radicands

A radical is a symbol used to indicate the root of a number, most commonly the square root.

To simplify a radical means to express it in its simplest form, removing any perfect square factors.

A negative radicand is a number under a radical sign that is less than zero, which results in an imaginary number when simplified.

√-1 is simplified to i, where i is the imaginary unit.

2i√6.

Factor 300 into its prime factors: 300 = 100 * 3 = 10^2 * 3, so √300 = 10√3.

2√6.

Factor 48 into 16 * 3, so √48 = √(16 * 3) = 4√3.

4√2.

Perfect squares can be factored out of a radical to simplify it.