Simplifying Radicals and Imaginary Numbers

​Unit 2 Review

Algebra 2​

​Sections

​

• 2.1 Square Root Function Graphs

• 2.2 Simplifying Radicals

• 2.3 Operations with Radicals

• 2.4 More Operations with Radicals

• 2.5 Imaginary Numbers

• 2.6 Exponent Rules

• 2.7 Rational Exponents

• 2.8 Negative Exponents

• 2.9 Solving Radical Equations​

Multiple Choice

Choose an accurate equation for the given graph:

• $$y=\sqrt[]{x+1}+2$$  

• $$y=\sqrt[]{x-1}+2$$  

• $$y=2\ \sqrt[]{x+1}$$  

• $$y=\sqrt[]{x-1}-2$$  

Multiple Choice

Based on the given graph, what is the value of "a"?

Vertex Form: $$y=a\ \sqrt[]{x-h}+k$$  

• 1

• -5

• 3

• 2

Multiple Choice

Simplify $$\sqrt[]{72}$$  .

• $$2\ \sqrt[]{6}$$  

• $$36\ \sqrt[]{2}$$  

• $$6\ \sqrt[]{2}$$  

• $$3\ \sqrt[]{8}$$  

Multiple Choice

Simplify $$\sqrt[]{45}+2\ \sqrt[]{20}$$  .

•   $$7\ \sqrt[]{5}$$  

• $$2\ \sqrt[]{5}$$  

• $$5\ \sqrt[]{2}$$  

• $$6\ \sqrt[]{5}$$  

Multiple Choice

Simplify $$\sqrt[]{7}\left(\sqrt[]{10}+\sqrt[]{7}\right)$$  .

• $$\sqrt[]{70}+7$$  

• $$\sqrt[]{17}+\sqrt[]{14}$$  

• $$\sqrt[]{70}+\sqrt[]{49}$$  

Fill in the Blanks

The following is equivalent to a single number. Type that number into the box.

$2^{\frac{7}{2}}\cdot2^{\frac{1}{2}}$  

Multiple Choice

Simplify and convert the following to a radical:

$$\left(x^{\frac{1}{4}}\right)^{\frac{7}{5}}$$  

• $$\sqrt[5]{x^2}$$  

• $$\sqrt[9]{x^7}$$  

• $$\sqrt[9]{x^8}$$  

• $$\sqrt[20]{x^7}$$  

Multiple Choice

Simplify $$\sqrt[]{-64}$$  

• $$4i$$  

• $$8i$$  

• $$4i\ \sqrt[]{4}$$  

• $$i\ \sqrt[]{64}$$  

Multiple Choice

When simplifying $$\sqrt[]{-2}\cdot\ \sqrt[]{-7}$$  , what is the next step?

• $$\sqrt[]{14}$$  

• $$i\ \sqrt[]{2}\cdot i\ \sqrt[]{7}$$  

• $$\sqrt[]{2i}\cdot\sqrt[]{7i}$$  

Multiple Choice

Simplify $$\left(5i\right)\left(-9i\right)$$  .

• -45i

• -45

• 45

• 45i

Multiple Choice

Simplify $$4\ \sqrt[3]{3}\left(\sqrt[3]{9}+2\sqrt[3]{2}\right)$$  .

• $$11\sqrt[3]{2}+\sqrt[]{9}$$  

• $$4\sqrt[3]{12}+2\sqrt[3]{5}$$  

• $$12+8\ \sqrt[3]{6}$$  

Fill in the Blanks

Simplify $\left(2+5i\right)-\left(-7+i\right)$  .

Type your response into the box.

Example: "10-2i"

Multiple Choice

Simplify $$\frac{3x^{-2}y^{-8}}{x^{-4}y^3}$$  .

• $$\frac{x^6}{3y^{11}}$$  

• $$\frac{3x^2}{y^5}$$  

• $$\frac{3x^2}{y^{11}}$$  

• $$\frac{3y^5}{x^6}$$  

Multiple Choice

Simplify $$\sqrt[3]{24x^6y^4z^9}$$  

• $$8x^2z^3\sqrt[3]{3y^4}$$  

• $$2x^2yz^3\sqrt[3]{y}$$  

• $$x^2z^3\sqrt[3]{24y^4}$$  

• $$2x^2yz^3\sqrt[3]{3y}$$  

Multiple Choice

Simplify $$\left(81x^4y^{11}\right)^{\frac{1}{4}}$$  completely as a radical.

• $$3xy^2\sqrt[4]{y^3}$$  

• $$3x\sqrt[4]{y^{11}}$$  

• $$3xy^7$$  

Fill in the Blanks

Solve $\sqrt[3]{2x+11}=-3$  . Type your answer value into the box. If the answer is no solution, type "ns".

Multiple Choice

Rationalize:

$$\frac{6}{7\ \sqrt[]{6}}$$  

• $$\frac{\sqrt[]{7}}{6}$$  

• $$\frac{\sqrt[]{6}}{7}$$  

• $$\frac{7\ \sqrt[]{6}}{6}$$  

Multiple Choice

Multiply and simplify:

$$\left(3-2i\right)\left(4+i\right)$$  

• 12-2i

• 14-5i

• 9+2i

• 23

That's it!​

• ​Use this as a "simulation" of the test!

• You can replay the practice version in Canvas as much as you want!

• If a certain questions went poorly, study them!