2.1 Solving Radical Equations

I can solve radical equations and equations with rational exponents Essential standard I can solve radical equations and equations with rational exponents

Warm up Rewrite the rational expression into radical form, then simplify. 1) 4 3 2 2) 8 2 3 Can you simplify the rational expression without rewriting it as a radical?

Warm up Simplify 3) 16 3 2 4) 27 4 3 5) 25 5 2

Radical Equation A Radical Equation is an equation that has a variable in the radicand or a variable with a rational exponent. Give an example of each type of radical equation.

Extraneous solution What is an extraneous solution?

Got it? Solve the radical equation

Rational Exponents Isolate the part of the equation with the rational exponent Raise each side of the equation to the reciprocal power Simplify- when evaluating it’s generally easiest to do the root first then the power. Isolate the variable Check answers – some solutions may be extraneous (meaning they aren’t actually solutions, plug your solutions into the original equation to be sure that it works)

Problem 2b What is the solution of 3 𝑥+1 3 5 +1=25

Solve the equation

Problem 3A What is the solution of 𝑥+8 = 𝑥

Problem 3B 2𝑥+1 = 𝑥

Problem 4 What is the solution of 8𝑥−12 =𝑥. Check your solutions.

I can solve radical equations and equations with rational exponents Essential standard I can solve radical equations and equations with rational exponents