Radicals Solving Radical Equations

9/9/2013 Radicals 2 What is a radical ? Symbol representing a fractional power Radical with index: For roots other than second Index n corresponds to exponent   n 1 n

9/9/2013 Radicals 3 Radical Functions Definition: A radical function f(x) is defined by f(x) = x b for b = 1/n for some integer n ≥ 2 Examples: f(x) = x 1/2 f(x) = x 1/3 Radicals  x = x 3  =

9/9/2013 Radicals 4 Rational Exponent Equations Solve: 1. x 1/4 = x 1/3 – 5 = 1 3. n –2 + 3n –1 + 2 = 0 Radicals

9/9/2013 Radicals 5 Radical Equations Solve: Radicals = x + 1 x + 5   5x – 6 = x = + 3 3x + 4  x + 1 

9/9/2013 Radicals 6 Radicals and Extraneous Roots Solve: Radicals  4 – 3x = x + 8 Caution: Always check for extraneous solutions when raising radical expressions to EVEN powers =  x + 1x – 5  = x + 1  2x 

9/9/2013 Radicals 7 Think about it !