Algebra 2 Unit 5 Review

Simplifying Radicals

100

a. 

sqrt{1/64}

b.

-sqrt{1/64}

c.

root(3){-1/64}

a. 1/8

b. -1/8

c. -1/4

200

Solve: 

25y^2 + 16 = 17

1/5, -1/5

300

a. 

sqrt{250}

b. 

root(3)(250)

a. 

5sqrt{10}

b. 

5 root(3)(2)

400

2 sqrt(270a^3b^10)

6ab^5 sqrt{30a}

500

a. 

sqrt{3/8}

b. 

root{4}{3/8}

a. 

sqrt{6}/4

b.

root{4}{6}/2

600

root(3)(6c) * root(3)(8c^-5)

(2root(3)(6c^2))/c^2

Operations with Radicals

100

root{3}{24} - root{3}{56} + root{3}{81}

5 root{3}{3} - 2root{3}{7}

200

(\sqrt{5} + \sqrt{2})^2

7 + 2\sqrt{10}

300

sqrt{10a} - sqrt{5a}/sqrt{2} + \sqrt{(2a)/5}

(7sqrt{10a})/10

400

(5sqrt{6} + 3sqrt{2})(2sqrt{6} - 4\sqrt{3})

60 - 60\sqrt{2} + 12\sqrt{3} - 12\sqrt{6}

500

(2\sqrt{7} - \sqrt{3})/(\sqrt{7} + \sqrt{3})

(17 - 3sqrt(21))/4

600

\sqrt{x}/(\sqrt{x}+ \sqrt{y}) + \sqrt{y}/(\sqrt{x} - \sqrt{y})

(x+y)/(x-y)

Rational Exponents

100

a. 

(-125)^(-2/3)

b. 

-125^(-2/3)

a. 1/25

b. -1/25

200

(27^4)^{-1/3}

1/81

300

(root(6)(3) * root(3)(3))/root(4)(3)

root(4)(3)

400

root{4}{x}*root(6)(x) \div root(3)(x)

x^(1/12)

500

(x^2+4)^{2/3} + 1 = 26

11, -11

Solving Equations

100

root(3)(3m -2) + 5 = 1

-62/3

200

sqrt(5-2k) = k-3

No solution

2 is extraneous

300

sqrt(2x+5) - 2sqrt(2x) =1

2/9

400

5x = x sqrt(2) + 9

(45 + 9 sqrt{2})/23

500

sqrt{3y+4} = 2 + sqrt{y+2}

y = 7

-1 is extraneous

Complex and Imaginary Numbers

100

a. (3+5i)(3-5i)

b. (3+5i) - (3-5i)

a. 34

b. 10i

200

a. - √(15) * √(-25)

b.  √(-15) * √(-25)

a. -5i√(15)

b. -5√(15)

300

Solve: 

3/4x^2 + 12 =0

4i, -4i

400

a. 

i^45

b. 

i^91

c. 

i^68

a. i

b. -i

c. 1

500

(2+5i)/(sqrt{3}+\sqrt{6}i)

(2 \sqrt{3} + 5\sqrt{6})/9 +(-2\sqrt{6} + 5\sqrt{3})/9i

600

Show that 2+i is a solution to 

x^2 -4x + 5 =0

(2+i)^2 -4(2+i) + 5 =0

3 + 4i -8 -4i + 5 =0

0 = 0