Radical Expressions

Simplify +/- Radicals

100

 9sqrt5 + sqrt20

11sqrt5

200

7sqrt2 - 4sqrt18

-5sqrt2

300

-sqrt6 - 3sqrt45

-sqrt6 - 9sqrt5

400

NUMBER TRIVIA QUESTION: In "The Hunger Games," what district is Katniss from? 

District 12

500

root(3)24 - 2root(3)375

-8root(3)2

600

10root(4)5 + 7root(3)40 - root(3)320

10root(3)5 + 10root(4)5

Multiply Radicals

100

NUMBER TRIVIA QUESTION: How many teeth does an adult human typically have?

32

200

root(3)(-6x^5) times root(3)(18x^4)

-3x^3root(3)4

300

sqrt3(2 - sqrt24)

2sqrt3 - 6sqrt2

400

2sqrt3(sqrt27 - 8sqrt6)

18 - 48sqrt2

500

(10 + 3sqrt7)(10 - 3sqrt7)

37

600

(3 - 2sqrtk)^2

9 - 12sqrtk + 4k

Divide Radicals

100

(sqrt21)/(sqrt3)

sqrt7

200

(20sqrt270)/(4sqrt3)

15sqrt10

300

(3sqrt8)/(8sqrt5)

(3sqrt10)/20

400

(sqrt5 - sqrt6)/sqrt18

(sqrt10 - sqrt12)/6

500

(6 + 5sqrt2)/(4 + 3sqrt2)

3 - sqrt2

600

NUMBER TRIVIA QUESTION: What year did the Titanic sink?

1912

Rational Exponents

100

Rewrite in exponential form: 

root(4)(b^3)

b^(3/4)

200

Rewrite in radical form and simplify:

(256x)^(1/4)

4root(4)x

300

5r^3 times 2r^(1/2)

10r^3sqrt(r)

400

((54^(1/2))^(5/3))/54^(1/2)

3root(3)2

500

NUMBER TRIVIA QUESTION: What is the only NFL team to ever have a perfect season? (team and year!)

1972 Miami Dolphins

600

(m^2)/root(3)m

mroot(3)(m^2)

Solving Radical Equations

100

Solve for x.

-5 = (x + 7)^(1/2) - 11

x = 29

200

Solve for x.

(3x - 21)^(1/3) = (19 - x)^(1/3)

x = 10

300

NUMBER TRIVIA QUESTION: How many legs does a lobster have?

Ten

400

Solve for x.

17-2sqrt(3x + 10) = 1

x = 18

500

Solve for x.

sqrt(6x + 15) = c + 4

x = -1

600

Solve for x.

sqrt(19x + 24) = -5sqrtx

No solution

(x = 4 is an extraneous solution!)