Section P3 Radicals and Rational Exponents

Square Roots

Examples Evaluate

Simplifying Expressions of the Form

The Product Rule for Square Roots

A square root is simplified when its radicand has no factors other than 1 that are perfect squares.

Examples Simplify:

Examples Simplify:

The Quotient Rule for Square Roots

Examples Simplify:

Adding and Subtracting Square Roots

Two or more square roots can be combined using the distributive property provided that they have the same radicand. Such radicals are called like radicals.

Example Add or Subtract as indicated:

Example Add or Subtract as indicated:

Rationalizing Denominators

Rationalizing a denominator involves rewriting a radical expression as an equivalent expression in which the denominator no longer contains any radicals. If the denominator contains the square root of a natural number that is not a perfect square, multiply the numerator and the denominator by the smallest number that produces the square root of a perfect square in the denominator.

Let’s take a look two more examples:

Examples Rationalize the denominator:

Examples Rationalize the denominator:

Other Kinds of Roots

Examples Simplify:

The Product and Quotient Rules for nth Roots

Example Simplify:

Example Simplify:

Rational Exponents

Example Simplify:

Example Simplify: Notice that the index reduces on this last problem.

Simplify: (a) (b) (c) (d)

Simplify: (a) (b) (c) (d)