Name: _______________________ Date: ________ Period:____________
Algebra 2 CC/H ~ Review for Test on Irrationals
1. Simplify: (2 − 3√𝑥)2
2. Solve for x: √2𝑥 − 4 = 𝑥 − 2
3
3. Simplify:( √27𝑥 12 ) (√16𝑥 4 )
4. Rationalize:
1
7− √11
3
5. Express the sum in simplest radical form: √6𝑎4 𝑏 2 and
3
√162𝑎4 𝑏 2
6. Find the solution set: √𝑥 − 1 = 1 − 𝑥
3
7. Simplify: √64𝑎16
8. Determine the value(s) that make the following rational
expression undefined and simplify:
18 − 6𝑥
3𝑥 2 − 6𝑥 − 9
9. Express
4
3 − √2
as an equivalent fraction with a rational
denominator.
4
4
10. Simplify: √25𝑥 3 𝑦 7 ∙ √75𝑥 6 𝑦 3
11. Solve for x: √3𝑥 + 16 = 𝑥 + 2
3
1
2
4
12. Find the difference when 𝑥 2 −
5
2
𝑥2 −
3
4
𝑥 − 4 is subtracted from
𝑥+1.
13. The product of (3 − √5) and(3 − √5)is:
14. Express 5√3𝑥 3 − 2√27𝑥 3 in simplest radical form.
15. Solve: √𝑥 + 3 = 3 − 𝑥
**16. Find the solution(s).
√𝑥 − 3 + √𝑥 + 4 = 7
17. Express
5
3− √2
with a rational denominator, in simplest
radical form.
18. Simplify: 4𝑎𝑏√2𝑏 − 3𝑎√18𝑏 3 + 7𝑎𝑏√6𝑏
19. Simplify the radical expression:
1
2
√80𝑥𝑧 3
20. Simplify the radical expression: √36𝑥 4 𝑦 2
21. Simplify the expression: 3𝑥√90𝑥 2 ∙ 𝑦√2𝑦 2
22. Simplify the expression: (2 − √8)(2 + √8)
23. What is the solution set of the equation: 𝑥 +
24. Solve for x:
4
4𝑥
𝑥−3
=2+
3
12
𝑥−3
25. Simplify: √16𝑎4 𝑏 4 + √125 𝑎3 𝑏 3
42
𝑥
= 13 ?