Chapter 6 Test Review
6-1 Roots and Radical Expressions
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
6-3 Binomial Radical Expressions
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
6-8 Graphing Radical Functions
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.
b. Use your answer to part (a) to find the radius of
a sphere with volume 100 cubic inches. Round
to the nearest hundredth.
40. What are the lengths of the sides of the
trapezoid shown at the right if the
perimeter of the trapezoid is 17 cm?