Unit 4B Radicals

Homework

Name _________________

Test _________________

Honors Algebra 2 Name ___________________________

Unit 4B – Worksheet #1 Review of radical and rational exponents

Rewrite using exponents.

1. √7 2. √9𝑥3

3. 3 √5𝑦4 4. 7 √2𝑥

3

Rewrite using radicals.

5. 21

3 6. 𝑦2

3 7. 𝑒4

5 8. 𝑓9

5

Simplify completely. Leave your answer in the form of the original problem.

9. 9𝑥𝑦√128𝑥𝑦3 10. √923 11. ( √9

3)

2 12. 2√4𝑥

13. 5𝑦 ⋅ 25 14. 𝑥 (𝑥1

5) 15. 2(3)

2

2

16. 𝑥𝑦2(𝑥𝑦2)1

3

17. 2(64𝑥)1

2 18. 55 243y 19. 12 84 ( 5)m n

20. 12 63 64x y 21. 2 5b b ba c 22. 3 2x x xb c

23. 3

48 124

24. 3

3 5 25. 3 93

3 6 3

64

27

x y

x z

Add and subtract. Simplify completely.

26. 2 108 27 3 75 27. 2 50 5 7 3 18

28. 5 1 4

72 18 506 3 5

29. 3 48 1

125 16

30. 3 5 350 3 8x y xy xy 31. 3 3 6 4 848 3a b a b

Simplify by rationalizing denominators.

32. 2 5 2

10

33.

5

2 7 34.

2

3 2

Honors Algebra 2 Name _______________________

Unit 4B – Worksheet #2 Solving radical equations

Solve the equation. Check for extraneous solutions.

1. 5

32 64x 2. 3

2 3 11x

3. 3

2(3 12) 3 24x 4. 3

4( 2) 8x

5. 3

2 125x 6. 4

31

( 3) 6 142x

7. 2

33( 5) 9 18x 8. 3

3 52(4 13) 5 49x

Solve the following. Check for extraneous solutions.

9. x 3 2 10. 23 x 16

11. 2 x 3 x 2 12. x 1 6x 7 1

13. 33 2x 3 2 x 14. 3 2x 1 2 2x 1

15. 2x 1 x 1

Solve using a graphing calculator. Round solutions to the nearest tenth.

16. 2

x 1 2x 1

Identify whether each statement is always true (A), sometimes true (S), or never true (N).

Place the appropriate letter in the space given.

_____17. x 3 12 _____18. x 6 3 x _____19. 3x 6 0

_____20. 2 2x 3 4 1 _____21. 4 42 3x 3x 15

22. On a clear day, the approximate distance, d, in feet, that a sightseer standing at the top

of a building h feet tall can see is given by 𝑑 = 6397.2√ℎ.

(a) On a clear day, what distance, in feet, can a sightseer see from the top of a 900-foot

building? Give your answer to the nearest foot.

(b) Convert your answer from part (a) to miles. (Note: 1 mile equals 5280 feet.)

(c) How tall is a building from which a sightseer can see 32 miles on a clear day? Give your

answer to the nearest foot.

Honors Algebra 2 Name_______________________

Unit 4B Worksheet #3 Solving Radical Inequalities

Solve the following inequalities. Use a number line to show your solution and in interval and

write the final answer in interval notation.

1. 3x 4 2 2. 3x 4 2

3. x 2 4. 2x 1 3 0

5. 2x 1 3 0 6. 9x 7 14x

7. x x

Honors Algebra 2 Name______________________________

Unit 4B – Worksheet #4

State the domain and range of the following using interval notation:

1. 4 1y x 2. 3 10y x 3. 3 5y x

4. 1y x 5. 3 1 12y x

Graph the following functions (you must indicate AT LEAST 3 points on each graph). State

the domain and range of each function using interval notation.

6. 2y x 7. 5 1y x 8. 3 1y x

D: ___________ R: ___________ D: ____________ R: ____________ D: ____________ R: ____________

9. 1 4y x 10. 3 1 2y x 11. 2y x

D: ___________ R: ___________ D: ____________ R: ____________ D: ____________ R: ____________

,

Graph the following functions (you must indicate AT LEAST 3 points on each graph). State

the domain and range of each function using interval notation.

12. 7y x 13. 3 4y x 14. 32 4y x

D: ____________ R: ____________ D: ____________ R: ____________ D: ____________ R:

____________

15. 3 3 4y x 16. 4 4 5y x 17. 3y x

D: ____________ R: ____________ D: ____________ R: ____________ D: ____________ R:

____________

,

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

-5 -4 -3 -2 -1 1 2 3 4 5 6

-5

-4

-3

-2

-1

1

2

3

4

5

-10 -8 -6 -4 -2 2 4 6

-5

-4

-3

-2

-1

1

2

3

Find the equation of the function graphed. State domain and range.

18. f(x) = _______________ 19. y = __________________

D: ____________ R:_____________ D:______________ R:___________

20. y =___________________

D:_____________ R:______________

Write the equation for each square root graph.

21. 22.

Equation: ______________________________ Equation: ______________________________

23. 24.

Equation: ______________________________ Equation: ______________________________

Describe all transformations from the function ( )f x x to g x .

25. 1

3 22

g x x 26. 3 3 5g x x

Honors Algebra 2 Name __________________________

Unit 4B Review Radicals WS#5

Solve each equation. Show all work for credit. Remember to check for extraneous roots.

1. 3 2 5 3x 2. 7 4 9 13x

3. 3 33 4 2 17x x 4. 2 12 2x x

5. 54 3 1 6x 6. 1 5 9x x

7. (x + 3)2/3 = 16 8. 4x1/2 + 9 = 49

Solve the following inequalities. Use a number line and write final answer in interval notation.

9. 2 6 2x 10. 314 5

2x

Graph the following functions. Must be accurate. Graph your parent graph first.

11. f(x) = √−𝑥 + 4 (use at least 3 points) 12. 3( ) 1 4g x x (use at least five points)

13. ( ) 2 5h x x (use at least 3 points) 14. 3( ) 3 2p x x (use at least 5 points)

Write the equation for each function given the graph below.

15. 16.

17. Describe the transformation from the parent graph, f(x) = x . 3

( ) 2 52

f x x

18. Write the equation of a square root function that has been shifted left 3 units, stretched

vertically by a factor of 4, and reflected over the x-axis.

19. Write the equation of a cube root function that has been shifted down 1 and right 2

units, shrunk horizontally by a factor of 1

4, and reflected over the y-axis.

Solve the equation. Check for extraneous roots.

20. 34 2 11 12x 21. 126x x

22. 2 1 3x x 23. 4

3(3 1) 5 21x

Simplify the expression.

24. 5 3200 8a b ab 25.

15 8 3

1

3

x y z

x yz

26. 1 1 1

3 3 315 11 8a b a b a b

27. 4 48 5 43 32 5 162m mn n m n 28. 12

3 6 2 29.

13 12 12 153 3x y x y

30. 5

3

24

12

x

x 31.

1 13 7 9 35 3a b c a b c

32. Rewrite with rational exponents. 59( )mn