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Math Help - Radical times two other radicals(distributive property)

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    Radical times two other radicals(distributive property)

    I need help on the procedure and rules for these kinds of problems. Here are two examples from my book.

    (*=radical sign)

    *2 (*2 + *3)

    *3(*15 + *21)
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    \sqrt{2} \left(\sqrt{2} + \sqrt{3}\right)
    Just imagine a = \sqrt{2}, b=\sqrt{3}. This gives you: a(a+b) which is something you probably know how to do already.

    Just keep in mind that when multiplying two radicals, you can combine the numbers under it and put it under a single radical, i.e. \sqrt{a} \cdot \sqrt{b} = \sqrt{ab}

    \sqrt{3}\left(\sqrt{15} + \sqrt{21}\right)

    Try the same thing as above.
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    Quote Originally Posted by endlesst0m View Post
    I need help on the procedure and rules for these kinds of problems. Here are two examples from my book.

    (*=radical sign)

    *2 (*2 + *3)

    *3(*15 + *21)
    Distribute like you would any other number, and then use this property to simplify: \sqrt{a}\sqrt{b} = \sqrt{ab}, where a,\ b are nonnegative real numbers. Here is an example of the basic process:

    \sqrt{5}\left(\sqrt{5} - \sqrt{2}\right)

    = \sqrt{5}\sqrt{5} - \sqrt{5}\sqrt{2}

    = \sqrt{5\cdot5} - \sqrt{5\cdot2}

    = \sqrt{25} - \sqrt{10}

    = 5 - \sqrt{10}
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