Unit 3 Day 4. Solving Equations with Rational Exponents and Radicals

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1 Unit Day 4 Solving Equations with Rational Exponents and Radicals

2 Day 4 Warm Up You know a lot about inverses in mathematics we use them every time we solve equations. Write down the inverse operation for each of the following (there could be more than one correct answer) and then give a definition for inverse in your own words. If you get stuck, it may be helpful for you to write the expression out and think what you would do to solve an equation that had that expression on one side of the equation. Use the information from the table above to solve the following equations. Express your answers in simplified radical form. a. 5 b. x 64 4 An inverse is 2 ( y ) 6

3 Day 4 Warm Up ANSWERS Modeling with Exponential Functions: Solving Equations with Rational Exponents and Radicals An inverse is x 7 adding 7 to a number x * /2 multiply by 2 x * 2/5 multiply by 5/2 x/ multiply by x 2 x x 5 5 x 2 x 5 take square root squaring a number raising to the /5 power raising to the 5 th power raising to the 5/2 power

4 Day 4 Warm Up ANSWERS Use the information from the table above to solve the following equations. Express your answers in simplified radical form. a. b. 5 x 64 5 x 64 x x x x x ( y ) ( y ) ( 6) y y y y y

5 Day 4 Warm Up ANSWERS An Inverse is??? 5

6 Homework Answers ~ Packet Page 5-6 Evens OR OR ( ) OR

7 Homework Answers ~ Packet Page 5-6 Evens Continued x (6p) 2 _OR_6 2 2 p a _ OR _ a a a (6x) _OR_ x 0. n 2 7

8 You Try! Notes p a 2 b 6 b a a a 5. 64x 52x 9 x x x 5x x 9 x 8 9. xy 4

9 Notes p. 9 Mixed Review: Simplify each expression.. 75y 2 27 y 45y. 2 8a b 6 b 2 2 y 5y 6ab 6b 2. 08yz 98yz 2 55yz z y 2z 2 y 2z 55y 9 4. x y 2 8x y 6x 4 6

10 Tonight s Homework: Packet pg. 7 0

11 Notes p. 0 Express final answers as radicals! Before partner work, let s do two together! = leave as a decimal HINT: We ll use the Inverses we discussed during today s warm-up! Do st Together Do st Together

12 Notes p. 0 Express final answers as radicals! = leave as a Work with a partner decimal Decide who will be Partner A and who will be Partner B ,500,000 2,500,

13 Yesterday s problems only had one step. However, today there are multiple steps, meaning that one cannot just simplify the radical or rational exponent until it is isolated on one side of the equation. Inverse You can isolate the radical using. There are also some problems below in which the rational exponent or radical is applied to the entire side of the equation. Only in these situations will you undo the rational exponents or radicals first. Before solving the entire problem, make sure you know what the first step will be

14 Steps To Solving Equations With Rational Exponents AND Radicals Radical. We ll do one of these in a minute! Rational Exponent Isolate the Term with the Rational Exponent (Get that term Alone) 2Do the Inverse Operation (Raise both sides to the reciprocal power) Solve for the variable 4Check the solution -Extraneous solution? Or Actual Solution? Or No Solution? 4

15 Solving with Rational Exponents and Radicals Lesson Isolate the Term with the Rational Exponent (Get that term Alone) 2Do the Inverse Operation (Raise both sides to the reciprocal power) Solve for the variable 4Check the solution -Extraneous solution? Or Actual Solution? Or No Solution? 4. x 2 We ll try a couple together! x 6 2 x = 625 x = 5

16 You Try! Finish these on Notes pg x 5207 x = x x x = x 5 5 = leave as a decimal 7.8 x = x 5 0 x = (2x 7) x = 6

17 Steps To Solving Equations With Rational Exponents AND Radicals Radical Isolate the Term with the Radical (Get that term Alone) 2Do the Inverse Operation (Raise both sides to the Index) Solve for the variable 4Check the solution -Extraneous solution? Or Actual Solution? Or No Solution? 7

18 Solving with Rational Exponents and Radicals Lesson Isolate the Term with the Radical (Get that term Alone) 2Do the Inverse Operation (Raise both sides to the Index) Solve for the variable 4Check the solution -Extraneous solution? Or Actual Solution? Or No Solution? We ll try a couple together! We ll do the bottom two!. 2x x 5 0 x = 4 8 x = 208

19 One more example A tougher one! Solve x 0 x x = 0 9

20 You Try! Finish Notes pg. = leave as a decimal._ x - 2 = 4 2._ x +2-2 =2 x = 66 x = 94 20

21 Whiteboard Practice! Send a partner to pick up the following each person needs of these: whiteboard marker eraser 2

22 . Solve for x. x 2 4 x 66 22

23 2. Solve for a. a x 94 2

24 . Solve for x. x 2 x 24 24

25 4. Solve for x. x 5 5 x 0 25

26 5. Solve for x. x 7 9 No solution! Always check your answers! 26

27 6. Solve for x. 6 x 2 2 x 27

28 7. Solve for x. 0 x x 2 x 2 28

29 8. Solve for y. 2 y x 9 29

30 9. Solve for b. 5 4b 2 0 x 4 0

31 Homework: Packet pg. 7

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