Exponents and Radicals

Combining Radical Expressions
Radical expressions can only be combined if there are like terms-terms with the same index and same radicand
(the expression inside the radical).

In the above expression, the terms with are alike and the terms with are alike. Therefore, the above
expressions simplifies as follows:

Notice that the two remaining terms are not alike and, hence, cannot be simplified.

Some terms which do not look alike at first glance may be alike after simplifying. Therefore, it is important
that you simplify all radicals before combining like terms.

Examples:

(note that these terms are NOT alike even though they both have a 10)

In simplifying we begin by using Property then simplifying and
rationalizing the denominator before combining:

(Note that 8 = 4 • 2)
(Multiply both by )

(now get a common denominator)

(now combine radicals)