Definition:  A radical expression is defined as any expression containing a radical (√) symbol. Many people mistakenly call this a ‘square root’ symbol, and many times it is used to determine the square root of a number. However, it can also be used to describe a cube root, a fourth root or higher.

Example of like radicals: 3√2x, √2x

Non-example of like radicals: ⁴√7a, ⁴√7b

Multiplication:
To multiply radical expressions, use the product property of radicals, distributive property, or FOIL method and simplify the radicands.

Product property of radicals: ⁿ√a • ⁿ√b = ⁿ√ab

Division:
To divide radical expressions, use the quotient rule for radicals and rationalize the denominator to simplify if necessary. Rationalizing the denominator:

If an expression contains a radical in the denominator, it is not simplified. To do so, multiply by a fraction equal to 1 that will eliminate the radical in the denominator. When the radical in the denominator is part of a binomial, rationalizing the denominator involves multiplying by a fraction equal to 1 made up of the conjugate. Solution:

Taking the fourth root of 16 in the first term allows us to rewrite this as:  Step 3: Simplify 