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Math Help - "rationalize the denominator and simplify"

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    "rationalize the denominator and simplify"

    i need help on this question that says rationalize the denominator and simplify.

    this is the problem::

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  2. #2
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    Quote Originally Posted by needleandthread View Post
    i need help on this question that says rationalize the denominator and simplify.

    this is the problem::

    + 1
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    Multiply by it's conjugate where the conjugate is the same numbers with the opposite sign between them:

    \frac{\sqrt3 +1}{\sqrt{3}+\sqrt{2}}

    The conjugate is \sqrt{3}-\sqrt{2}

    \frac{\sqrt3 +1}{\sqrt{3}+\sqrt{2}} \cdot \frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}-\sqrt{2}} = \frac{(\sqrt{3} +1)(\sqrt{3}-\sqrt{2})}{(\sqrt{3}+\sqrt{2})(\sqrt{3}-\sqrt{2})}

    Use the difference of two squares on the denominator
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  3. #3
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    Quote Originally Posted by needleandthread View Post
    i need help on this question that says rationalize the denominator and simplify.

    this is the problem::

    + 1
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    thank you
    multiply by \frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}+\sqrt{2}}
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