Download in simplest form?

Algebra II – Chapter 8 Test Review
Standards/Goals:
 A.SSE.2: I can take the structure of an expression and identify different ways to
rewrite it
 I can use the FOIL method to multiply binomials that have radical expressions.
 I can multiply binomial expressions using conjugates.
 N.RN.2: I can rewrite expressions involving radicals and rational exponents using the
properties of exponents.
 A.REI.2: I can solve simple rational and radical equations in one variable.
 I can show how to arrive at ‘extraneous’ solutions.
 A.CED.4.: I can rearrange formulas to highlight a quantity of interest, using the same
techniques and methods as you would use to solve an equation.
 F.BF.1.b.: I can combine standard function types using arithmetic operations, such as
addition, subtraction, multiplication, and division.
 F.BF.1.c.: I can use the idea of composition to evaluate radical functions.
 F.BF.4.a.: I can solve an equation for a simple function that has an inverse.
 I can write an expression for the inverse of a simple function.
 F.IF.7.b.: I can graph square and cube root functions.
 I can determine the transformations of the graph of a radical function.
1. What is the real cube root of -216?
81
2. What is the real fourth root of − ?
625
3.
4.
5.
6.
What is the simplified form of the expression: √81𝑥 12 𝑦 26 ?
What is the simplified form of the expression √112𝑥 9 𝑦10 ?
3
3
What is the simplest form of √48𝑤𝑧 4 √4𝑤 2 ?
What is the simplest form of 5√63 − 3√18?
7. What is the simplest form of
√45𝑥 7
√125𝑥𝑦 4
?
8. What is the simplest form of (2 – 3√5)(3 + 4√5)?
9
9. What is the simplest form of
?
1
3
4
3
3 + √7
10.What is 𝑤 𝑧 in simplest form?
11.Let f(x) = -3x + 16 and g(x) = 2𝑥 2 .
a. What is (g – f)(x)?
b. What is the domain of (g – f)(x)?
𝑔
c. What is the domain of (x)?
𝑓
d. What is g ᵒ f (x)?
e. What is f ᵒ g(x)
f. What is f ᵒ g(-3)?
12. What is the inverse of y = -2(x + 6)?
13. Consider the following function:
𝑦 = −3√𝑥 + 9 − 16
a. What is the domain for the function given in the previous problem?
b. What are the transformations for the following function?
4
14. What is the DOMAIN of
?
5−√𝑥+10
15. Rationalize the denominator and simplify:
5+√10
5+√2
16. Simplify the following expression:
3
4
√216𝑤 7 √81𝑦 8
√12𝑤 12 𝑦 6
17. Simplify the following expression: √
25𝑟 4 𝑠 5
48𝑡 5
18. Suppose that a, b, and c are real numbers where 𝑏 = 𝑐 3 and 𝑎 = 𝑏 5 .
Write the following in terms of c:
4
4
√𝑐𝑎 + √𝑏 6
19. Solve the following:
a. √5𝑥 − 2 − 7 = 3
b. √5𝑥 − 2 + 7 = 3
1
c. 3𝑥 2 − 10 = 2
d. √3𝑥 + 7 = 𝑥 − 1
e. √3𝑥 = √𝑥 + 6
20. Simplify:
2 + √5−3𝑥
3−√𝑥+7
21. A spherical water tank holds 9000 square feet of water. What is the
3
6𝑉
diameter of the tank? (Use the formula: 𝑑 = √ )
𝜋