20-1 Radicals

Radical

Expressions​

By OLIVIA GREEN

• The opposite of a root is an exponent!

  ​To simplify SQUARE ROOTS:

  • Write the radicand as a product of numbers, one of which is a PERFECT SQUARE.

  • Find the square root of the perfect square.​

Radical Expressions

Basics/Square Roots

Multiple Choice

What is the inverse operation of an exponent?

• multiplying

• finding the root

• dividing

• finding the base

Multiple Choice

$$\sqrt[]{36}$$  

• 9

• 6

• 4

• 8

• NOT ALL SQUARE ROOTS ARE PERFECT!

  • When this happens you should follow the same process ,but you will need to leave any remaining products that cannot come out of the radical​ underneath the root.

Radical Expressions

Basics/Square Roots

Multiple Choice

$$\sqrt[]{18}$$  

• $$3\sqrt[]{2}$$  

• $$2\sqrt[]{9}$$  

• $$2\sqrt[]{3}$$  

• $$\sqrt[]{9}$$  

​Expon

• ​To simplify CUBE ROOTS:

  • Write the radicand as a product of numbers, one of which is a PERFECT CUBE.

  • Find the cube root of the perfect cube.​

Radical Expressions

Cube Root & Beyond

Multiple Choice

$$\sqrt[3]{64}$$  

• 32

• 4

• 8

• 2

Multiple Choice

$$\sqrt[3]{54}$$  

• $$3\sqrt[3]{18}$$  

• $$2\sqrt[3]{3}$$  

• $$3\sqrt[3]{2}$$  

• $$18\sqrt[3]{3}$$  

Fractional Exponents can be written as radical expressions!

Bottom

Index

Top

Exponent​

Radical Expressions

Fractional Exponents

Open Ended

What does B.I.T.E stand for?

Multiple Choice

$$13^{\frac{1}{4}}$$  

• $$\sqrt[]{13}$$  

• $$\sqrt[4]{13}$$  

• $$\left(\sqrt[4]{13}\right)^2$$  

• $$3\sqrt[3]{2}$$  

Multiple Select

$$7^{\frac{3}{5}}$$ This fractional exponent can be written in TWO ways! Select two choices! 

• $$\left(\sqrt[3]{7}\right)^5$$  

• $$\left(\sqrt[5]{7}\right)^3$$  

• $$\sqrt[3]{7^5}$$  

• $$\sqrt[5]{7^3}$$  

Multiple Choice

Write the following as a radical expression: $$x^{\frac{3}{2}}$$  

(Be careful! ;)

• $$\sqrt[]{x^3}$$  

• $$\sqrt[2]{x^3}$$  

• $$\sqrt[3]{x^2}$$   

• $$\left(\sqrt[3]{x}\right)^2$$  

Shoulder Partners Time!

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Explain to your partner what you got out of today's lesson. What did you learn? Then, let your shoulder partner explain what they learned from class today!​

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The shoulder partner with the shortest hair goes first! ​

Time to Practice!

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Turn to pg. 303 in your textbook and work out problems 10-16 on a loose leaf piece of paper.

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Whatever is not completed in class is for HOMEWORK tonight!​