Radicals Lesson

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!