Unit 4 Circles: Review of Radicals

Unit 4 Circles: Review of Radicals

By Stephanie Balbaneda

​Please take out your:

• Laptop

Notebook

Pencil​

Radicals

​By the end of the day students will be able to

• ​Simplify

• Add & Subtract

• Multiply

• ​Rationalize

Simplify

• Make a factor tree

• List the factors under the radical sign

• Circle the pairs of numbers

• Pairs come outside the radical sign (only once)

• Multiply the remaining terms

Multiple Choice

What is the first step for simplifying radicals?

• Multiply remaining terms?

• Circle the pairs of numbers

• Make a factor tree

• Bring pairs outside the radical (only once)

• List factors under the radical

Multiple Choice

Simplify $$\sqrt{56}$$  

• $$2\sqrt{14}$$  

• $$4\sqrt{14}$$  

• $$2\sqrt{28}$$  

• $$2\sqrt{9}$$  

Add and Subtract

• Simplify First

• Combine like terms (terms with the same radicand)

• ONLY outside numbers are added (radicans DO NOT change once they are simplified)

Multiple Select

What kind of terms can be added or subtracted? (Check all that apply)

• Like terms

• Common terms

• Terms with the same radicand

​Evaluate the following radicals:

Examples:​

Multiple Choice

Add

$$\sqrt{2}+3\sqrt{2}$$  

• $$2\sqrt{2}$$  

• $$3\sqrt{4}$$  

• $$4\sqrt{2}$$  

• $$4\sqrt{4}$$  

Multiple Choice

Add

$$\sqrt{27}+2\sqrt{12}$$  

• $$3\sqrt{3}+4\sqrt{6}$$  

• $$7\sqrt{3}$$  

• $$12\sqrt{3}$$  

• $$7\sqrt{6}$$  

Multiply

• Multiply the outside numbers

• Multiply the inside numbers

• Simplify

Multiple Select

What do you do after you multiply the outside terms and the inside terms?

• Simplify

• Multiply

• Nothing

Examples:​

Multiple Choice

Multiply

$$2\sqrt{12}\times3\sqrt{7}$$  *Remember to simplify*

• $$6\sqrt{84}$$  

• $$5\sqrt{19}$$  

• $$12\sqrt{21}$$  

• $$8\sqrt{10}$$  

Multiple Choice

$$\sqrt[]{15}\cdot4\sqrt[]{3}$$  

• $$12\sqrt[]{5}$$  

• $$3\sqrt[]{5}$$  

• 45

• $$3\sqrt[]{2}$$  

Multiple Choice

$$\sqrt[]{10}\cdot\sqrt[]{10}$$  

• 10

• $$4\sqrt[]{30}$$  

• 100

• $$2\sqrt[]{5}$$  

*Be Careful*

• Adding or Subtracting : SIMPLIFY FIRST

• Multiplying : SIMPLIFY LAST

Multiple Choice

When do you simplify FIRST?

• Multiplying

• Adding and Subtracting

How To Simplify

The purpose is to factor out a perfect square.

Perfect squares like 4, 9, 16, 25, 36, 49.... come out to whole numbers when their square roots are taken. To simplify we want to break apart into factors that include at least one perfect square. Then this number can leave the square root (evaluate).

Some text here about the topic of discussion

Multiple Choice

$$3\sqrt[]{20}\cdot3\sqrt[]{20}$$  

• $$24\sqrt[]{10}$$  

• 20

• 40

• 180

Multiple Choice

Simplify: $$\sqrt[]{192}$$  

• $$8\sqrt[]{5}$$  

• $$3\sqrt[]{3}$$  

• $$8\sqrt[]{3}$$  

• $$4\sqrt[]{2}$$  

Rationalizing the Denominator

The objective is to have no square roots in the denominator. To do that we perform multiplication to the ratio that will remove the square root (cancel it) from the denominator.

Subject | Subject

Rationalize the Denominator

Multiple Choice

Simplify: $$\frac{2}{\sqrt[]{2}}$$  

• $$\sqrt[]{2}$$  

• $$\frac{15}{5}$$  

• $$\frac{2\sqrt[]{5}}{3}$$  

• $$\frac{\sqrt[]{2}}{2}$$  

Multiple Choice

Simplify: $$\frac{\sqrt[]{2}}{4\sqrt[]{3}}$$  

• $$\frac{\sqrt[]{15}}{9}$$  

• $$\frac{2\sqrt[]{3}}{3}$$  

• $$\frac{\sqrt[]{6}}{12}$$  

• $$2\sqrt[]{6}$$  

Multiple Choice

Rationalize the denominator. $$\frac{\sqrt{3}}{\sqrt{15}}$$  

• $$\frac{\sqrt{5}}{5}$$  

• $$\frac{\sqrt{3}}{12}$$  

• $$\frac{5\sqrt{2}}{2}$$  

• $$\frac{\sqrt{3}}{3}$$  

Multiple Choice

Rationalize the denominator. $$\frac{\sqrt{4}}{\sqrt{5}}$$  

• $$\frac{\sqrt{10}}{5}$$  

• $$\frac{2\sqrt{5}}{5}$$  

• $$\frac{\sqrt{5}}{2}$$  

• $$\frac{\sqrt{15}}{3}$$  

Multiple Choice

Rationalize the denominator. $$\frac{4}{\sqrt{5}}$$  

• $$\frac{4\sqrt{5}}{5}$$  

• $$\frac{\sqrt{5}}{4}$$  

• $$\frac{\sqrt{6}}{3}$$  

• $$\frac{5\sqrt{2}}{2}$$