Simplifying Radicals Review

Simplifying Radicals Review

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...

Multiple Choice

Which of the following is NOT a perfect square?

• $\sqrt{625}$

• $\sqrt{169}$

• $\sqrt{800}$

Remember...

Simplifying perfect squares means giving the integer, that when multiplied by itself is equal to the value inside the radical...


example:   $\sqrt{64}\ =\ 8$  

because...  $8\cdot8\ =\ 64$  

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... >

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!

Yo. Check it...

 $\sqrt{x}=\ \sqrt{x}$  

 $\sqrt{x^2}=\ \sqrt{x\cdot x}$  

 $\sqrt{x^2y^3}=\ \sqrt{x\ \cdot x\ \cdot\ y\ \cdot\ y\ \cdot\ y}$  

 $\sqrt{8m^2n^5}=\ \sqrt{2\cdot2\cdot2\cdot m\cdot m\cdot n\cdot n\cdot n\cdot n\cdot n}$  

Multiple Choice

Factor $\sqrt{x^5y^3}$  

•  $\sqrt{x\cdot x\cdot x\cdot y\cdot y\cdot y}$  

•  $\sqrt{x\cdot x\cdot x\cdot x\cdot x\cdot y}$  

•  $\sqrt{x\cdot x\cdot x\cdot x\cdot x\cdot y\cdot y\cdot y}$  

So how do we deal with something like...

Example...

factor and pull out the doubles...

Multiple Choice

Factor: $\sqrt{x^3}$  

•  $\sqrt{3x}$  

•  $\sqrt{x\cdot x\cdot x}$  

•  $\sqrt{x\cdot x}$  

Multiple Choice

Simplify: $\sqrt{x\cdot x\cdot x}$  

•  $x\sqrt{x}$  

•  $x^2\sqrt{x}$  

•  $x\sqrt{x^2}$  

Multiple Choice

Factor: $\sqrt{8m^2n^4}$  

•  $\sqrt{8\cdot m\cdot m\cdot n\cdot n\cdot n\cdot n}$  

•  $\sqrt{4\cdot2\cdot m\cdot m\cdot n\cdot n\cdot n\cdot n}$  

•  $\sqrt{2\cdot2\cdot2\cdot m\cdot m\cdot n\cdot n\cdot n\cdot n}$  

Multiple Choice

Simplify: $\sqrt{2\cdot2\cdot2\cdot m\cdot m\cdot n\cdot n\cdot n\cdot n}$  

•  $2n^2\sqrt{2m^2}$  

•  $2mn\sqrt{2n}$  

•  $2mn^2\sqrt{2}$  

Multiple Choice

Simplify: $\sqrt{3x^6}$  

•  $3x^3$  

•  $x^3\sqrt{3}$  

•  $x^2\sqrt{3x}$