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

Rationalize the denominator. Simplify the answer. $\frac{5\ +\sqrt{3}}{2\ -\sqrt{3}}$   

•  $13\ +7\sqrt{3}$  

•  $-13\ +7\sqrt{3}$  

•  $13\ -7\sqrt{3}$  

•  $13\ +\sqrt{3}$  

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CCSS.HSN.RN.A.2

Rationalize the denominator. Simplify the answer. $\frac{3\ +\sqrt{8}}{2\ -\ 2\sqrt{8}}$   

•  $\frac{11\ -8\sqrt{2}}{14}$  

•  $\frac{11\ +8\sqrt{2}}{14}$  

•  $\frac{11-\sqrt{2}}{14}$  

•  $\frac{11\ +\ 8\sqrt{2}}{-14}$  

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CCSS.HSN.RN.A.2

Rationalize the denominator. Simplify the answer. $\frac{4\ +\sqrt{6}}{\sqrt{2}\ +\sqrt{3}}$   

•  $\sqrt{3}\ -\sqrt{2}$  

•  $2\sqrt{3}\ -\ \sqrt{2}$  

•  $\sqrt{3}+2\sqrt{2}$  

•  $2\sqrt{3}+\sqrt{2}$  

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CCSS.HSN.RN.A.2

Rationalize the denominator. Simplify the answer. $\frac{4\ +\sqrt{27}}{2\ -3\sqrt{27}}$   

•  $\frac{89\ +42\sqrt{3}}{239}$  

•  $\frac{-89\ +42\sqrt{3}}{-239}$  

•  $\frac{89\ +21\sqrt{3}}{239}$  

•  $\frac{89\ +42\sqrt{3}}{-239}$  

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CCSS.HSN.RN.A.2

Rationalize the denominator. Simplify the answer. $\frac{5\ -\ \sqrt{21}}{\sqrt{3}\ -\ \sqrt{7}}$   

•  $\frac{\sqrt{3}\ +\sqrt{7}}{2}$  

•  $\frac{\sqrt{3}+7}{-2}$  

•  $\frac{\sqrt{3}-\ \sqrt{7}}{2}$  

•  $\frac{\sqrt{3}\ -2\sqrt{7}}{10}$  

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CCSS.HSN.RN.A.2

Rationalize the denominator. Simplify the answer. $\frac{6\ +\sqrt{15}}{4\ -\sqrt{15}}$   

•  $39\ -\ 10\sqrt{15}$  

•  $-39\ +10\sqrt{15}$  

•  $-39\ -\ 10\sqrt{15}$  

•  $39\ +10\sqrt{15}$  

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CCSS.HSN.RN.A.2

Rationalize the denominator. Simplify the expression. $\frac{2\ -\sqrt{3}}{4\ +\sqrt{3}}$   

•  $\frac{11\ +6\sqrt{3}}{13}$  

•  $\frac{11\ -6\sqrt{3}}{13}$  

•  $\frac{-11\ +\sqrt{3}}{13}$  

•  $\frac{-11\ +2\sqrt{3}}{13}$  

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CCSS.HSN.RN.A.2

Rationalize the denominator. Simplify the answer. $\frac{5}{4\sqrt{7}\ +5}$   

•  $\frac{20\sqrt{7}\ -\ 25}{87}$  

•  $\frac{-20\sqrt{7}\ +25}{87}$  

•  $\frac{-20\sqrt{7}\ -25}{87}$  

•  $\frac{10\sqrt{7}-5}{87}$  

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CCSS.HSN.RN.A.2

Rationalize the denominator. Simplify the answer. $\frac{\sqrt{2}\ +\sqrt{3}}{\sqrt{2}\ -\ \sqrt{3}}$   

•  $5\ +2\sqrt{6}$  

•  $5\ -\ 2\sqrt{6}$  

•  $-5\ -2\sqrt{6}$  

•  $-5\ +\sqrt{6}$  

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CCSS.HSN.RN.A.2