# Arithmetic of Irrational Expressions

The arithmetic of irrational expressions is just like the arithmetic of algebraic expressions. Like terms can be added to and subtracted from simpler expressions, but unlike terms cannot. For example, 3*x* + 5*x* = 8*x*, but 3*x* + 5y cannot be simplified. Like and unlike terms can be multiplied and divided. For example, (3*x*)(5*x*) = 15*x*2, and (3*x*)(5*y*) = 15*xy*.

Similarly,

cannot be simplified because the**—the terms under the radical—are different.**

*radicands*Simplify:

At first look you might think that these terms cannot be combined because the radicands are different. However, if you simplify

to beSimplify:

. The third term in the problem is different in that there is a fraction within the square root. Simplifying the fraction makes**), and**

*rationalizing the denominator*Simplify:

These are cube roots, so you need to be thinking about perfect cubes when simplifying terms.

andTo rationalize the denominator of a term in which the denominator is a binomial, such as

, multiply the numerator and denominator by the conjugate of the given denominator, thus using the formula for the difference of two squares.Rationalize the denominator of

, and simplify the fraction.