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Math Help - [SOLVED] Surds

  1. #1
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    [SOLVED] Surds

    Q. simpify: \sqrt a^3 + 2 \sqrt a
    the answer is (a+2)\sqrt a but but i can't seem to figure out the solution.

    thanks
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  2. #2
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    Quote Originally Posted by waven View Post
    Q. simpify: \sqrt a^3 + 2 \sqrt a
    the answer is (a+2)\sqrt a but but i can't seem to figure out the solution.

    thanks

    a^{\frac{3}{2}}+2a^{\frac{1}{2}}

    Take out the common factor which is a^{\frac{1}{2}}

    a^{\frac{1}{2}}(a+2) which is similar the ans given.
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  3. #3
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    Quote Originally Posted by mathaddict View Post
    a^{\frac{3}{2}}+2a^{\frac{1}{2}}

    Take out the common factor which is a^{\frac{1}{2}}

    a^{\frac{1}{2}}(a+2) which is similar the ans given.
    is a^{\frac{1}{2}} the common factor because there are 2 a^{\frac{1}{2}}s?
    and
    would it still be the same answer it it was \sqrt a(a+2) rather than (a+2)\sqrt a
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  4. #4
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    Quote Originally Posted by waven View Post
    is a^{\frac{1}{2}} the common factor because there are 2 a^{\frac{1}{2}}s?
    and
    would it still be the same answer it it was \sqrt a(a+2) rather than (a+2)\sqrt a
    yes .

    note that ab = ba
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  5. #5
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    Quote Originally Posted by mathaddict View Post
    a^{\frac{3}{2}}+2a^{\frac{1}{2}}

    Take out the common factor which is a^{\frac{1}{2}}

    a^{\frac{1}{2}}(a+2) which is similar the ans given.
    btw how did a^{\frac{3}{2}} change to (a+2)
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  6. #6
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    Quote Originally Posted by waven View Post
    btw how did a^{\frac{3}{2}} change to (a+2)
    a^{\frac{3}{2}} = a^{1 + \frac{1}{2}} = a \cdot a^{\frac{1}{2}}.
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