1. IT’S RADICAL!! SOLVING RADICAL EQUATIONS

2. SIMPLE RADICAL EQUATIONS – FIRST STEPS GIVEN: 1.Make sure the radical is on one side of the equation and the regular numbers are on the other side. 2.Square BOTH sides to remove the radical.

3. YOU TRY!!

4. SLIGHTLY MORE COMPLICATED Same rules: GIVEN: 1.Make sure radical is on one side and regular numbers are on the other side. 2.Square both sides and solve.

5. YOU TRY!

6. YOU TRY AGAIN…

7. WHAT IF THERE IS A COEFFICIENT ON THE RADICAL?

8. WHAT IF THE RADICAL ISN’T A SQUARE ROOT?

9. WHAT IF THERE ARE RADICALS ON BOTH SIDES?

10. YOU HAVE TO CHECK YOUR ANSWERS Sometimes you get an EXTRANEOUS solution. That means you can get something for an answer algebraically that will NOT work when you plug it back in. Check out the previous problem. The answer is -3, but when you plug it back in to the ORIGINAL equation you get: Hmmm….We don’t take square roots of negative numbers…yet. Therefore… -3 is EXTRANEOUS.

11. YOU TRY!! CHECK: Because there is a negative number under the radical, the solution is EXTRANEOUS. Your answer is NO REAL SOLUTION.

12. YOU TRY AGAIN CHECK: Because this is a true statement and the answer is a REAL number, your answer of x = 15 is good.

13. YOU TRI (HAHA—3 RD PROBLEM) 1. ANSWER: CHECK: NO REAL SOLUTION – a positive square root cannot equal a negative number. WHEN YOU ARE GIVEN A RADICAL, YOU ARE ALSO GIVEN THE SIGN. THESE HAVE TO MATCH UP.

14. DID I MENTION? WHEN YOU ARE GIVEN A RADICAL, YOU ARE ALSO GIVEN THE SIGN. THESE HAVE TO MATCH UP. IT IS IMPORTANT!!

15. FINALLY…THE LAST ONE 2. ANSWER: Check: NO REAL SOLUTION because the square root of a negative number is not a real number.