5-8 RADICAL EQUATIONS & INEQUALITIES Objectives Students will be able to: 1) Solve equations containing radicals 2) Solve inequalities containing radicals

Radical Equations…. - Are equations that have variables in the radicand. - Must be CHECKED ! - May have extraneous solutions : solving algebraically may yield an answer that does not satisfy the original equation.

To solve an equation that contains radicals… raise BOTH SIDES of the equation to a power equal to the index of the radical. (This will eliminate the radical.)

Example 1 : Solve each equation. Check your solution(s). 1) 2)

3) 4)

5) Try these. 6) 7)

RADICAL INEQUALITIES Solving radical inequalities is similar to solving radical equations, however there are a few things to keep in mind… 1) when dividing or multiplying both sides of the inequality by a negative, you need to reverse the inequality sign. 2) when the index of the root is even (ex. square root), identify the values of the variable for which the radicand is nonnegative. This is important because there is no real root of a negative radicand with an even index

Example 2 : Solve each inequality. 1)2)

Try These! 3)4)

Concept Summary To solve radical inequalities, complete the following steps: 1) If the index of the root is even, identify the values of the variable for which the radicand is nonnegative. 2) Solve the inequality algebraically. 3) Test values to check your solution.

Homework Text p. 266 #s 14 – 36 even #s 39 – 41 all