Solving problems involving mixed operations on radicals

Rationalize each denominator. Simplify the answer. $\frac{4}{1\ +\sqrt{3}}$   

•  $2\ -2\sqrt{3}$  

•  $-2\ +2\sqrt{3}$  

•  $4\ -2\sqrt{3}$  

•  $-4\ -2\sqrt{3}$  

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CCSS.HSN.RN.A.2

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CCSS.HSN.RN.A.2

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CCSS.HSN.RN.A.2

Rationalize the Denominator:

 $\frac{\sqrt{3}}{2+4\sqrt{3}}$  

•  $\frac{\sqrt{3}+6}{22}$  

•  $22+\sqrt{3}$  

•  $6+\sqrt{22}$  

•  $\frac{-\sqrt{3}+6}{22}$  

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CCSS.HSN.RN.A.2

Simplify the expression.

 $\frac{5\sqrt{16}}{\sqrt{5}}$  

•  $4\sqrt{5}$  

•  $\frac{\sqrt{80}}{5}$  

•  $20\sqrt{5}$  

•  $\frac{4\sqrt{5}}{5}$  

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CCSS.HSN.RN.A.2

 $\frac{1}{2+\sqrt{3}}$  

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•  $2\ -\ \sqrt{3}$  

•  $\frac{\sqrt{3}}{2}$  

•  $\frac{1}{\sqrt{3}}$  

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CCSS.HSN.RN.A.2

Given:

 $A=\sqrt{3}$  

 $B=2\sqrt{3}$  
 $C=\sqrt{25}$  
 $D=\sqrt{16}$  
Which answer choices result in a rational number.
Select ALL that apply.

•  $A+B$  

•  $C+D$  

•  $A\cdot B$  

•  $C\cdot D$  

•  $A\cdot A$  

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CCSS.HSN.RN.A.2

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CCSS.HSN.RN.A.2

 $\sqrt{20}\left(4+\sqrt{10}\right)$  

•  $8\sqrt{5}+10\sqrt{2}$  

•  $4\sqrt{20}+10\sqrt{2}$  

•  $2\sqrt{10}+10\sqrt{2}$  

•  $4\sqrt{5}+10\sqrt{2}$  

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CCSS.HSN.RN.A.2

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• √5
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• -2√15

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CCSS.HSN.RN.A.2