simplifying Radicals

simplifying Radicals

Examples

•  $\sqrt{10}=\sqrt{2}\cdot\sqrt{5}$  

•  $\sqrt{18}=\sqrt{9}\cdot\sqrt{2}=3\sqrt{2}$  

Multiple Choice

 $\sqrt{15}=\sqrt{5}\cdot\sqrt{3}$  True or False?

• True

• False

Multiple Choice

 $\sqrt{50}=25\sqrt{2}$  True or False?

• True

• False

Multiple Choice

Simplify

 $\sqrt{24}$  

•  $4\sqrt{6}$  

•  $2\sqrt{6}$  

•  $6\sqrt{2}$  

•  $6\sqrt{4}$  

Simplify   $\sqrt{80}$  

​
  

•  $\sqrt{80}=\sqrt{16\cdot5}=4\sqrt{5}$  

• But you might not notice that at first. 

• You can also factor 80 and pull pairs of factors out of the radicand.

•  $\sqrt{80}=\sqrt{8\cdot10}=\sqrt{4\cdot2\cdot2\cdot5}=2\sqrt{2\cdot2\cdot5}=2\cdot2\sqrt{5}=4\sqrt{5}$  

Multiple Choice

√28

• 7√2

• 7√4

• 4√7

• 2√7

Multiple Choice

√45

• 3√5

• 5√3

• 9√5

• 5√9

Multiple Choice

√96

• 16√6

• 2√6

• 4√6

• √2

Multiple Choice

√125

• 5√5

• 25√5

• 5√25

• 5√2

Multiple Choice

√216

• 6√4

• 4√6

• 36√6

• 6√6