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Math Help - Rationals

  1. #1
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    Rationals

    Help please? these are just examples of the equations i need to solve...please help =)

    How do i simplify...

    2\sqrt 150 \over \sqrt 8

    Simplify by rationalizing the denominator

    \sqrt 32 \over \sqrt 18

    Express the following with rational denominators

    \sqrt 7 - \sqrt 2 \over \sqrt 2

    Simplify and express in lowest terms

    10 \sqrt 18 - 5 \sqrt 24 \over \sqrt 5

    any help would be appreciated! THANK YOU!
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  2. #2
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    \begin{array}{rcl}<br />
 \frac{{10\sqrt {18}  - 5\sqrt {24} }}{{\sqrt 5 }} & = & \frac{{10\sqrt {2 \cdot 9}  - 5\sqrt {4 \cdot 6} }}{{\sqrt 5 }} \\ <br />
  & = & \frac{{30\sqrt 2  - 10\sqrt 6 }}{{\sqrt 5 }} \\ <br />
  & = & \frac{{30\sqrt {10}  - 10\sqrt {30} }}{5} \\ <br />
  & = & 6\sqrt {10}  - 2\sqrt {30}  \\ <br />
 \end{array}<br /> <br />
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  3. #3
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    Hello, nathan02079!

    2\sqrt 150 \over \sqrt 8
    We have: . 2\sqrt{\frac{150}{8}} \;=\;2\sqrt{\frac{75}{4}} \;=\;2\frac{\sqrt{75}}{2} \;=\;\sqrt{75} \;=\;\sqrt{25\cdot3} \;=\;\sqrt{25}\cdot\sqrt{3} \;=\;5\sqrt{3}


    Simplify by rationalizing the denominator:

    \sqrt 32 \over \sqrt 18
    We have: . \frac{\sqrt{32}}{\sqrt{18}} \;=\;\sqrt{\frac{32}{18}} \;=\;\sqrt{\frac{16}{9}} \;=\;\frac{\sqrt{16}}{\sqrt{9}} \;=\;\frac{4}{3}


    Express the following with rational denominators

    \sqrt 7 - \sqrt 2 \over \sqrt 2
    Rationalize: . {\color{blue}\frac{\sqrt{2}}{\sqrt{2}}}\cdot\frac{  \sqrt{7} - \sqrt{2}}{\sqrt{2}} \;=\;\frac{\sqrt{14} - 2}{2}

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