Rationalizing Surds

Simplify by rationalizing the denominator:

(Hint: rewrite without a surd on the denominator)

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Simplify by rationalising the denominator:

(Hint: Rewrite without surds in the denominator)

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Expand and simplify ...

(2 + √3)(3 + √3)

• 9 + 5√3

• 6 + 6√3

• 9 + √3

• 15 + 5√3

Expand and simplify ...

(3 + 2√2)(1 + 3√2)

• 15 + 11√2

• 15 + 5√2

• 5 + 11√2

• 5 + 5√2

To rationalize the denominator of this expression you need to multiply by

• $\frac{4}{4}$

• $\frac{\sqrt{3}}{\sqrt{3}}$

• $\frac{4}{\sqrt{3}}$

• $\frac{\sqrt{3}}{4}$

Rationalize the denominator:
 $\frac{1}{4\sqrt{10}}$  

•  $\frac{\sqrt{1}}{4}$  

•  $\frac{\sqrt{10}}{40}$  

•  $\frac{1}{4}$  

•  $\frac{\sqrt{10}}{400}$  

Express the following division without any surds in the denominator.

•  $\frac{\sqrt{7}}{2}$ 

• $\sqrt{2}$

•  $\frac{\sqrt{14}}{2}$ 

•  $\frac{\sqrt{14}}{7}$ 

• cannot be done

Rationalize the denominator:
 $\frac{\sqrt{5}}{2\sqrt{3}}$  

•  $\frac{\sqrt{15}}{6}$  

•  $\frac{\sqrt{15}}{18}$  

•  $\frac{5\sqrt{3}}{6}$  

•  $\frac{5\sqrt{3}}{18}$  

 $\frac{10+8\sqrt{7}}{\sqrt{31}}$  

•  $\frac{3\sqrt{221}}{16}$  

•  $\frac{8\sqrt{31}+11\sqrt{217}}{31}$  

•  $\frac{10\sqrt{31}+8\sqrt{217}}{31}$  

•  $\frac{10\sqrt{33}+8\sqrt{231}}{33}$  

Fully simplify...

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