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Math Help - square roots

  1. #1
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    Red face square roots

    hi

    can you help me to resolve a square root task?
    i have marked square roots with S-letters.
    _____________________________________________

    1 / S3 * ( S3 + 3 / S2 * S3 ) * S2

    _____________________________________________

    cecilia
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  2. #2
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    Quote Originally Posted by Cecilia6 View Post
    hi

    can you help me to resolve a square root task?
    i have marked square roots with S-letters.
    _____________________________________________

    1 / S3 * ( S3 + 3 / S2 * S3 ) * S2

    _____________________________________________

    cecilia
    Do you mean:

    \dfrac1{\sqrt{3} \cdot \left( \sqrt{3} + \frac3{\sqrt{2} \cdot \sqrt{3}} \right) \cdot \sqrt{2}}

    If so: Expand the bracket in the denominator:

    \dfrac1{3 \cdot \sqrt{2}+3}=\dfrac1{3(\sqrt{2} + 1)} = \dfrac{\sqrt{2}-1}3
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  3. #3
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    no, that's not what i meant it's difficult to mark it better than i did it, because i don't know how to type the right marks
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  4. #4
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    Square Roots

    Hello Cecilia6
    Quote Originally Posted by Cecilia6 View Post
    hi

    can you help me to resolve a square root task?
    i have marked square roots with S-letters.
    _____________________________________________

    1 / S3 * ( S3 + 3 / S2 * S3 ) * S2

    _____________________________________________

    cecilia
    Let me have another guess then! Perhaps you mean

    \frac{1}{\sqrt{3}} \times \left(\sqrt{3} + \frac{3}{\sqrt {2} \sqrt{3}}\right) \times \sqrt{2}

    If that's it, then you can simplify it like this:

    \frac{1}{\sqrt{3}} \times \left(\sqrt{3} + \frac{3}{\sqrt {2} \sqrt{3}}\right) \times \sqrt{2}

    = \frac{\sqrt{2}}{\sqrt{3}}\times \frac{\sqrt{3}\sqrt{2}\sqrt{3}+3}{\sqrt{2}\sqrt{3}  }

    = \frac{\sqrt{2}}{\sqrt{3}}\times \frac{3\sqrt{2}+3}{\sqrt{2}\sqrt{3}}

    = \frac{\sqrt{2}\times 3(\sqrt{2}+1)}{3\sqrt{2}}

    = \sqrt{2} + 1

    Grandad
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  5. #5
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    Hello, Cecilia!

    Knowing the way the inexperienced expresses division,
    . . I think I know what the problem says.


    \frac{1}{\sqrt{3}}\left(\frac{\sqrt{3} + 3}{\sqrt{2}\cdot\sqrt{3}}\right)\sqrt{2}

    We can reduce immediately: . \frac{1}{\sqrt{3}}\left(\frac{\sqrt{3}+3}{{\color{  red}\rlap{///}}\sqrt{2}\cdot\sqrt{3}}\right){\color{red}\rlap{///}}\sqrt{2}

    . . . =\;\frac{1}{\sqrt{3}}\left(\frac{\sqrt{3}+3}{\sqrt  {3}}\right) \;= \;\frac{\sqrt{3}+3}{\sqrt{3}\cdot\sqrt{3}} \;=\;\frac{\sqrt{3}+3}{3}

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