# Aim: How do we solve radical equations?

## Presentation on theme: "Aim: How do we solve radical equations?"— Presentation transcript:

Aim: How do we solve radical equations?
Do Now: Describe the steps for solving: x2 – 80 = 0 x2 = 80 add 80 to both sides take square root of both sides simplify Describe the reverse process square both sides x2 = 80 x2 – 80 = 0 subtract 80 from both sides How do we solve? solve by first squaring both sides.

Perfect Squares 12 144 11 121 100 10 9 81 8 64 7 49 6 36 5 25 4 16 3 9 4 2 1

Simplifying Radicals KEY: Find 2 factors for the radicand - one of which is the largest perfect square possible Multiplying Radicals

Dividing Radicals If quotient is not a perfect square you must simplify the radicand.

Solve and check: Isolate the radical: (already done) Square each side: Solve the derived equation: x2 – 9x + 16 = 0 use quadratic formula:

Solve and check: Isolate the radical: (already done) Square each side: Solve the derived equation: x – 2 = 25 x = 27 Check: (x – 2)1/2 = 5 [(x – 2)1/2]2 = 52 alternate: 5 = 5

? Extraneous Roots Solve and check: Isolate the radical:
Square each side: Solve the derived equation: 2y – 1 = 9 2y = 10 y = 5 Check: y = 5 is an extraneous root; there is no solution! ? 3 + 7 = 4

Solve and check: Isolate the radical: Square each side: Solve the derived equation: x2 – 2x + 1 = x + 5 x2 – 3x – 4 = 0 (x – 4)(x + 1) = 0 x = x = -1 Check each root: ? 4 = 4 x = -1 is an extraneous root