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Math Help - More problems

  1. #1
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    More problems

    Simplify:

    (2 - a^{2}) \cdot \frac {\sqrt {a + \sqrt {2} }} {\sqrt {(\sqrt {2} + a)^{3}}}, a > \sqrt {2}

    This one, too:

    x^{n-1} \cdot (x^{n})^{2-n}
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by p.numminen View Post
    Simplify:

    (2 - a^{2}) \cdot \frac {\sqrt {a + \sqrt {2} }} {\sqrt {(\sqrt {2} + a)^{3}}}, a > \sqrt {2}
    <br />
(2 - a^{2}) \frac {\sqrt {a + \sqrt {2} }} {\sqrt {(\sqrt {2} + a)^{3}}}=<br />
(2 - a^{2}) \frac {(a + \sqrt {2})^{1/2}} {(\sqrt {2} + a)^{3/2}}=<br />
(2 - a^{2}) \frac {1} {(\sqrt {2} + a)}=\sqrt{2}-a<br /> <br />
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  3. #3
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    How exactly do you get

    \sqrt{2}-a out of (2 - a^{2}) \frac {1} {(\sqrt {2} + a)} ?
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  4. #4
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    Hello, p.numminen!

    Simplify: . (2 - a^{2}) \cdot \frac {\sqrt {a + \sqrt {2} }} {\sqrt {(\sqrt {2} + a)^{3}}},\;\;a > \sqrt {2}

    We have: . (2-a^2)\cdot \frac{(\sqrt{2}+a)^{\frac{1}{2}}} {(\sqrt{2}+a)^{\frac{3}{2}}}\;\;=\;\;\frac{2-a^2}{\sqrt{2}+a}

    The numerator factors: . \frac{(\sqrt{2} - a)(\sqrt{2} + a)}{\sqrt{2} + a}. . . . . and we can cancel.

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