Investigating Roots

Roots

Square Roots

has two equal factors

Square Root Examples

•  $\sqrt{16}$  

•  $\sqrt{\frac{16}{25}}$  

•  $\sqrt{-4}$  

Poll

What is

$$\sqrt{81}$$  ?

• 9

• 81

• 27

Poll

b² = 100

• b = 100

• b = 10

• b = 50

Poll

$$\sqrt{x}$$  = 5 

• x = 25 

• x = 5 

Cube Roots

•  $cubed\ root\ of\ -27$  

•  $cubed\ root\ of\ 8$  

Poll

What is the cubed root of 125?

• -5

• 5

• 25

Poll

The cubed root of -1000

• -10

• 10

• -100

Approximating Square Roots

Find two perfect, consecutive squares that the number is between

Estimate

 $\sqrt{8}$   to the nearest integer

• The square root of 8 is not a whole number because 8 is not a perfect square. 

• What two perfect squares is  $\sqrt{8}$   between? 

•  $\sqrt{4}$    $<$   $\sqrt{8}$   $<$   $\sqrt{9}$  

• 2 <  $\sqrt{8}$  < 3

Poll

Estimate

$$\sqrt{33}$$  

• 25 <  $$\sqrt{33}$$   < 36

• 33

• 5 <  $$\sqrt{33}$$  < 6

Poll

Estimate

$$\sqrt{2}$$  

• 2

• 2 and 3 

• 1 <  $$\sqrt{2}$$  <  2

Poll

Estimate

$$\sqrt{83}$$  

• 81 <  $$\sqrt{83}$$  < 100

• 9 <  $$\sqrt{83}$$  < 10

Poll

Estimate

$$\sqrt{15}$$  

• 15

• 3 <  $$\sqrt{15}$$  < 4 

• 4 <  $$\sqrt{15}$$  < 5 

Poll

On a scale of 1- 3, how to do you feel about solving problems with roots?

• 1 - LOST

• 2 - Still have some questions and need some help

• 3 - I'm good!