6.2 Radicals and Rational Exponents

A radical is a mathematical expression that contains a square root, cube root, or nth root of a number.

• Factor the radicand (the number under the radical) as much as possible. For example, the radicand of 16x4 is 4x2, because 16x4 can be factored as (2^2)(x^2)^2.

• Any factor that appears in the radicand to an even power can be removed from the radical and put as a positive exponent outside of the radical. For example, the radicand of 16x4 can be written as (2^2)(x^2)^2, so the radical can be simplified to 2x^2.

• If the radicand is a product of two numbers, the radical can be simplified by combining the radicals. For example, the radicand of (4x2)(2x2) can be written as 4x2 * 2x2, so the radical can be simplified to 2(x^2)^2, or 2x^4.