# Chapter 6 Test Review

```Chapter 6 Test Review
Simplify
6-4 Rational Exponents
Write each expression in simplest form.
2
3
20. 𝑦 5 ∙ 𝑦 8
4
21. (3𝑥
2.
√121𝑦10
22.
3.
5
1. √𝑝12 𝑞4
1
12𝑥 3
1
4𝑦 2
√243𝑥 5 𝑦15
6-2 Multiplying and Dividing Radical Expressions
Multiply and simplify.
2
1⁄
2 )(4𝑥 ⁄3 )
6-5 Solving Square Root and Other Radical Equations
Solve. Check for extraneous solutions.
4. √−9𝑥 2 𝑦 4 ∙ 3√12𝑥𝑦
23. √𝑥 + 1 = 𝑥 − 1
5
24. 2√5𝑥 + 2 = 3
5. √12𝑥 2 𝑦 ∙ √3𝑥𝑦 4
25. √7𝑥 − 6 − √5𝑥 + 2 = 0
6. 4√2𝑥 ∙ 3√8𝑥
26. (2𝑥 − 4)2 = 10 − 𝑥
3
Divide and simplify. Rationalize the denominator, if
needed.
3
√18𝑦 2
7.
3
√12𝑦
162𝑎
8. √ 6𝑎3
3𝑎
3
9. √4𝑏2 𝑐
Simplify if possible.
10. 3√32 + 2√50
4
4
11. 3√32 − 2√162
3
12. 14 √𝑥𝑦 − 3 3√𝑥𝑦
13. (1 − √5)(2 − √5)
14. (√2 + √7)2
Rationalize the denominator and simplify the answer.
16.
6-6 Function Operations
𝑥
Let 𝑓(𝑥) = −3𝑥 + 2, 𝑔(𝑥) = 5, ℎ(𝑥) = −2𝑥 2 + 9, and
𝑗(𝑥) = 5 − 𝑥. Find each value or expression.
27.
28.
29.
30.
31.
(𝑓 ∘ 𝑗)(3)
𝑓(𝑥) − ℎ(𝑥)
(ℎ ∘ 𝑔)(−5)
(𝑔 ∘ 𝑓)(𝑎)
(ℎ ∙ 𝑗)(𝑥)
6-7 Inverse Relations and Functions
Find the inverse of each function. Is the inverse a
function? Describe the domain and range of the inverse.
32. 𝑦 = (𝑥 + 4)2 − 4
33. 𝑓(𝑥) = √3𝑥
Multiply
15.
1
2+√14
√7+√2
3
2+ √𝑥
3
√𝑥
Simplify
17. √28 + 4√63 − 2√7
18. 6√45𝑦 2 + 4√20𝑦 2
19. 6√40 − 2√90 − 3√160
1
5
34. 𝑓(𝑥) = − 𝑥 + 2
Graph each function using transformations.
3
35. 𝑦 = − √8𝑥 − 56 + 4
36. 𝑦 = √25𝑥 + 75 − 1
1
37. 𝑦 = 4 √𝑥 − 1 + 5
Word Problems
38. The formula s = 0.04n + 2500 gives an
employee’s monthly salary s, in
dollars, after selling n dollars in
merchandise at an appliance store.
a. Find the inverse of the function. Is the inverse a
function?
b. Use the inverse to find the amount of
merchandise sold if the employee’s salary was
\$2820 last month.
39. The volume of a sphere of radius r is
4
V   r3
3
a. Use the formula to find r in terms of V.
Rationalize the denominator.