Simplifying Radicals Review

Simplifying Radicals Review

​

Remember...

Multiple Choice

Which of the following has an answer of 14?

• $$\sqrt{196}$$

• $$\sqrt{200}$$

• $$\sqrt{28}$$

• $$\sqrt{7}$$

Multiple Choice

...and which has an answer of 100?

• $$\sqrt{10}$$

• $$\sqrt{200}$$

• $$\sqrt{10,000}$$

• $$\sqrt{50}$$

Remember, some radicals are not perfect...

​

But...

Simplifying non-perfect radicals means "rescuing all the perfect squares you can from under the radical by factoring and leaving the rest behind...

Example... >

Multiple Choice

Which of the following is NOT a perfect square?

• $$\sqrt{625}$$

• $$\sqrt{169}$$

• $$\sqrt{800}$$

Then...

So...

​

Multiple Choice

Which is the prime factorization of $$\sqrt{20}$$  ?

• $$\sqrt{10\ +\ 10}$$  

• $$\sqrt{5\cdot2\cdot2}$$  

• $$\sqrt{10\cdot2}$$  

Multiple Choice

Rewrite $$\sqrt{5\cdot2\cdot2}$$  

• $$5\sqrt{4}$$  

• $$4\sqrt{5}$$  

• $$2\sqrt{5}$$  

Multiple Choice

Which shows the prime factoring of  $$2\sqrt{40}$$  ?

• $$\sqrt{2\cdot2\cdot2\cdot5}$$  

• $$2\sqrt{2\cdot10}$$  

• $$2\sqrt{2\cdot2\cdot2\cdot5}$$  

Multiple Choice

Simplify: $$2\sqrt{2\cdot2\cdot5}$$  

• $$4\sqrt{10}$$  

• $$2\sqrt{5}$$  

• $$4\sqrt{5}$$  

Multiple Choice

Simplify:  $$-3\sqrt{84}$$  

• $$-12\sqrt{80}$$  

• $$-6\sqrt{21}$$  

• $$2\sqrt{21}$$  

Simplify Radical Expressions with Variables...

YOU CAN DO THIS!

Multiple Choice

Factor: $$\sqrt{x^3}$$  

• $$\sqrt{3x}$$  

• $$\sqrt{x\cdot x\cdot x}$$  

• $$\sqrt{x\cdot x}$$  

Example...

factor and pull out the doubles...

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

√28

• 7√2

• 7√4

• 4√7

• 2√7

Multiple Choice

√45

• 3√5

• 5√3

• 9√5

• 5√9

Multiple Choice

Simplify

$$\sqrt{24}$$  

• $$4\sqrt{6}$$  

• $$2\sqrt{6}$$  

• $$6\sqrt{2}$$  

• $$6\sqrt{4}$$  

Examples

Multiple Choice

Which of the following is a perfect square?

• 12
• 90
• 40
• 64

Multiple Choice

Which of the following in NOT a perfect square?

• 49

• 81

• 111

• 144

Multiple Choice

Simplify the following radical: √32

• 3√2
• 4√8
• 16√2
• 4√2

Multiple Choice

Simplify the following radical: √28

• 7√2
• 7√4
• 4√7
• 2√7

Multiple Choice

Simplify the following radical: √72

• 8√3
• 6√2
• 3√8
• 4√8

Multiple Choice

Simplify the following radical: √80

• 16√5
• 2√20
• 4√5
• 8√5