Numbers Systems - Complete

Fully simplify....

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Fully simplify....

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What should you multiply $\frac{6}{1-\sqrt{5}}$  by to rationalize the denominator?

• -4

•  $1-\sqrt{5}$  

•  $1+\sqrt{5}$  

•  $-\frac{\left(3-3\sqrt{5}\right)}{2}$  

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

•  $\frac{\sqrt{6}-\sqrt{10}}{8}$  

•  $\frac{\sqrt{6}-\sqrt{10}}{-2}$  

•  $\frac{\sqrt{6}+\sqrt{10}}{8}$  

•  $\frac{2\sqrt{3}+2\sqrt{5}}{-2}$  

 $\frac{-2}{1+\sqrt{6}}$  Rationalize the following:

•  $\frac{1+\sqrt{6}}{-2}$  

•  $\frac{-2+2\sqrt{6}}{-5}$  

•  $-\frac{2\sqrt{6}}{6}$  

•  $-2\sqrt{6}$  

 $\frac{3+5\sqrt{3}}{4-2\sqrt{3}}$  Rationalize:

•  $\frac{-9+7\sqrt{3}}{2}$  

•  $\frac{-18+14\sqrt{3}}{4}$  

•  $\frac{21+13\sqrt{3}}{2}$  

•  $\frac{24-26\sqrt{3}}{4}$  

 $\frac{\sqrt{3}-\sqrt{7}}{\sqrt{3}+\sqrt{7}}$  

•  $\frac{5-\sqrt{21}}{-2}$  

•  $\frac{10-\sqrt{21}}{-2}$  

•  $\frac{5-2\sqrt{21}}{-2}$  

•  $-\frac{4}{10}=-\frac{2}{5}$  

1.       If a and b are positive integers, which of the following is/are correct?


 $I.\sqrt{a^2+b^2}=a+b$  

 $II.\sqrt{a^2b^2}=ab$  
 $III.\sqrt{2a^2b}\times\sqrt{6a^3b}=2a^2b\sqrt{3a}$  

• II only

• III only
  

• II and III only
  

• I, II and III

 $2√32-√50+√98$  

•  $√2$  

•  $10√2$  

•  $56√2$  

•  $700√2$  

• A

• B

• C

• D