Algebra 2 Unit 3: Radicals and Complex Numbers

Simplifying radicals, rational exponents, radical equations, and adding, multiplying and dividing complex numbers. 12 questions. Have a go at each one on paper before you tap "Show me how".

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Question 1

Simplifying radicalsNo calculator

Simplify $\sqrt{72}$.

1. $36\sqrt{2}$
2. $8\sqrt{3}$
3. $6\sqrt{2}$
4. $2\sqrt{6}$

Question 2

Adding radicalsNo calculator

Simplify $2\sqrt{12}+5\sqrt{3}$.

1. $7\sqrt{3}$
2. $7\sqrt{15}$
3. $2\sqrt{17}$
4. $9\sqrt{3}$

Question 3

Rationalizing denominatorsNo calculator

Simplify $\frac{6}{\sqrt{3}}$.

1. $\frac{\sqrt{3}}{2}$
2. $3\sqrt{2}$
3. $2\sqrt{3}$
4. $6\sqrt{3}$

Question 4

Powers of iNo calculator

What is $i^{23}$?

1. $1$
2. $-i$
3. $i$
4. $-1$

Question 5

Complex arithmeticNo calculator

Multiply $(3+2i)(1-4i)$.

1. $3-8i$
2. $11-10i$
3. $11+10i$
4. $-5-10i$

Question 6

Complex arithmeticNo calculator

Write $\frac{5+i}{1-i}$ in the form $a+bi$.

1. $2+3i$
2. $2-3i$
3. $4+6i$
4. $3+2i$

Question 7

Complex solutionsNo calculator

Find the complex solutions of $x^2+4x+13=0$.

1. $x=2+3i \text{ or } x=2-3i$
2. $x=-2+6i \text{ or } x=-2-6i$
3. $x=-4+3i \text{ or } x=-4-3i$
4. $x=-2+3i \text{ or } x=-2-3i$

Question 8

Radical equationsNo calculator

Solve $\sqrt{x+7}=x+1$.

1. $x=2 \text{ or } x=-3$
2. $x=2$
3. $x=-3$
4. $x=3$

Question 9

Rational exponentsNo calculator

Solve $x^{\frac{3}{2}}=27$.

1. $x=9$
2. $x=18$
3. $x=81$
4. $x=3$

Question 10

Rational exponentsNo calculator

Simplify $(8x^6)^{\frac{1}{3}}$ for $x>0$.

1. $2x^{3}$
2. $8x^{2}$
3. $2x^{2}$
4. $\frac{8}{3}x^{2}$

Question 11

Complex numbersNo calculator

What is the absolute value of $6-8i$?

1. $14$
2. $10$
3. $100$
4. $-2$

Question 12

Radical equationsNo calculator

Solve $\sqrt[3]{2x-1}=3$.

1. $x=4.5$
2. $x=5$
3. $x=14$
4. $x=13$