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Aim: How do we solve radical equations?

x 2 = 80. x 2 = 80. x 2 – 80 = 0. Aim: How do we solve radical equations?. x 2 – 80 = 0. add 80 to both sides. Do Now: Describe the steps for solving:. take square root of both sides. simplify. Describe the reverse process. square both sides. subtract 80 from both sides.

yolanda-harding
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Aim: How do we solve radical equations?

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

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

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

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

  5. Must have same radicand and index • Add or subtract coefficients and combine result with the common radical Coefficient Common Radical ex. Adding/Subtracting Radicals Combined Result Unlike radicals must first be simplified to obtain like radicals (same radicand-same index), if possible.

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

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

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

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

  10. ? Square each side: Solve the derived equation: Solving Radical Equations Solve and check: 32(x – 2) = 22(x + 8) 9(x – 2) = 4(x + 8) 9x – 18 = 4x + 32 x = 10 x = 10 checks out as the solution

  11. Evaluate for 500: Evaluate for 545: Model Problem The radical function is an approximation of the height in meters of a female giraffe using her weight x in kilograms. Find the heights of female giraffes with weights of 500 kg. and 545 kg.  3.17 m.  3.27m.

  12. a. Model Problem The equation gives the time T in seconds it takes a body with mass 0.5 kg to complete one orbit of radius r meters. The force F in newtons pulls the body toward the center of the orbit. a. It takes 2 s for an object to make one revolution with a force of 10 N (newtons). Find the radius of the orbit. b. Find the radius of the orbit if the force is 160 N and T = 2.

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