Solving Radical Equations Section 12.3 September 27, 2016September 27, 2016September 27, 2016

Warm Up

Goals ► Solve a radical equation ► California State Standard 2: Understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents.

Key Terms ► Radical—a square root ► Extraneous solution—a trial solution that does not satisfy the original equation

Squaring both sides of an equation ► If a = b, then a 2 = b 2, where a and b are algebraic expressions. Example

Example 1

Example 2

Example 3

Example 4 ► Solve the equation and check for extraneous solutions

Example 5 ► The horizontal distance S (in meters) traveled by a projectile is related to its initial velocity (in m/sec) by the formula If v = 224 m/sec, find S.

Key Terms ► Cube root of a—If b 3 =a, then b is called the cube root of a. ► Radical notation—the n th root of a is written as ► Rational exponent—when you have a fraction in the exponent

Rational Exponents ► Let a be a nonnegative number, and let m and n be positive integers

Example 1 ► Find the following cube root or square root

Example 2 ► Rewrite the following expressions using rational exponent notation and radical notation.

Properties of Rational Exponents ► Let a and b be nonnegative real numbers and let m and n be rational numbers. a m a n = a m+n (a m ) n = a mn (ab) m = a m b m

Example 3 ► Evaluate the expression using the properties fractional exponents

Example 4 ► Simplify the variable expression using the properties of rational exponents

Homework ► Page 707 (4 – 32 even) ► Page 709 (5 - 13) ► Page 713 ( even)