Unit 4B Radicals - Weebly
Transcript of Unit 4B Radicals - Weebly
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