3/8- Section 6.2

Radicals and Exponents

Previously: Finding roots of a number

•  $\sqrt{25}=5,\ -5$  

• Why? 

•  $5\cdot5=25$  , or  $5^2=25$  

•  $-5\cdot-5=25$  , or  $\left(-5\right)^2=25$ 

Finding roots of a number

•  $8^{\frac{1}{3}}=2,\$ 

• Why?

•  $2\cdot2\cdot2=8$  , or  $2^3=8$  

Finding roots of a number

•  $-125^{\frac{1}{3}}=-5,\$ 

• Why?

•  $-5\cdot-5\cdot-5=-125$ , or  $\left(-5\right)^3=-125$  

Multiple Choice

What is the cube root of 1000?

 $1000^{\frac{1}{3}}$  =

• 10

• 100

• 1

• 3000

Fill in the Blanks

What is the fourth root of 81?

 $81^{\frac{1}{4}}$  =

Multiple Choice

What is the seventh root of 128?

 $128^{\frac{1}{7}}$  =

• 2

• -2

• 128/7

• 3

• 4

Fill in the Blanks

What is the cube root of -216?

 $-216^{\frac{1}{3}}$  =

Think about it!

What do you think is the square root of -16? You will give an answer on the next slide!

 $\sqrt{-16}=?$  

Open Ended

What is the square root of -16?

 $\sqrt{-16}=?$  

 $\sqrt{-16}=?$  

Note:

 $4\cdot4=16$  
and
 $-4\cdot-4=16$  

In a future course...

COMPLEX NUMBERS!