Topic 6: Rational Exponents, Radicals, and Complex Numbers

Simplifying Radicals

100

Simplify the expression. 

√(125x)

5√ (5x)

200

Simplify the expression. 

√(-225)

15i

300

Simplify the expression. 

2 √(147x³y³)

14xy √(3xy) 

400

Simplify the expression. 

∛(64x¹⁴y⁶)

4x⁴y² ∛ (x²)

500

Simplify the expression. 

√(64x²/16y³)

(2x) / (y√ (y))

or 

(2x√ y) / (y²)

Rationalizing the denominator

100

Rationalize the denominator. 

5 / √(3)

5√(3) / 3

200

Rationalize the denominator. 

√(x/5)

√(5x) / 5 

300

Rationalize the denominator. Don't forget to simplify. (hint: i²= -1)

1 / (3-i)

3+i / 10

400

Rationalize the denominator. 

5 / (5 - √2)

(10 + 2√2) / 23 

500

Rationalize the denominator. Don't forget to simplify. (hint: i²= -1)

(1+3i) / (2+i)

1+ i 

Solving Equations with Radicals

100

Solve for x. Check if your answer is extraneous or not.

 √(2x) = 4

x = 8 

non extraneous

200

Solve for x. Check if your solution is extraneous.

√(2x+3) - 3 = -2 

 x = -1

non-extraneous

300

Solve for n. Check if you solution is extraneous.

√(3n) = √(4n − 1)

n = 1

non extraneous

400

Solve for n. Check if you answer is extraneous or not. 

n − 7 = √(3n − 21)

x = 7 and 10

Both are non extraneous

500

Solve for m. Check if your solutions are extraneous. 

4 + √(-3m + 10) = m

No solution both answers are extraneous. 

m = 3 and 2

Complex Numbers Operations

100

Complete the following operation. Write your result as in general form. (a + bi) 

(9+2i) + (5-3i)

14 - i

200

Complete the following operation. Write your result as in general form. (a + bi)

(13-17i) - (9-14i)

4 - 3i

300

Complete the following operation. Write your result as in general form. (a + bi)

3i (2 - i)

3 + 6i

400

Complete the following operation. Write your result as in general form. (a + bi)

(7+3i)(5-2i)

41+i

500

Complete the following operation. Write your result as in general form. (a + bi)

(2 - 5i)²

-21-20i

Random Simplifying

100

Simplify. 

√(20)

2√5

200

Simplify. 

√(-16)

4i

300

Simplify. 

i¹⁶

-1

400

Simplify. 

i³⁴

-1

500

Simplify.

i^1485687

-i