Radicals

Radicals

What can we do with Radicals?

• Simplify

• Add & Subtract

• Multiply

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

Making a factor tree is the "prime factorization."

The numbers at the end of the "branches" of the factor tree are the factors.

Multiple Select

What is the prime factorization of

 $\sqrt{56}$ ?

• 2*4*7

• 2*2*2*7

• 4*7

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

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

Multiple Choice

Multiply

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

•  $6\sqrt{84}$  

•  $5\sqrt{19}$  

•  $12\sqrt{21}$  

•  $8\sqrt{10}$  

*Be Careful*

• Adding or Subtracting : SIMPLIFY FIRST

• Multiplying : SIMPLIFY LAST

• 
  

Multiple Select

Which of these involves simplifying? (Check all that apply)

• Simplifying

• Adding and Subtracting

• Multiplying

Multiple Choice

When do you simplify FIRST?

• Multiplying

• Adding and Subtracting

Pay attention to the signs. Know when you Add, Subtract, or Multiply!

It can get tricky. Don't rush!