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Math Help - Problem with Root

  1. #1
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    Problem with Root

    I don't understand how 3√2 = to √18.. and how to get rid of the root to become 3 x 2. Can anyone show me a few more examples also?

    Thank You
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  2. #2
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    Hello hovermet
    Quote Originally Posted by hovermet View Post
    I don't understand how 3√2 = to √18.. and how to get rid of the root to become 3 x 2. Can anyone show me a few more examples also?

    Thank You
    Two things you need to know about square roots:
    The definition of a square root: \sqrt{a}\times\sqrt{a} = a ...Rule 1

    How multiplication works with square roots: \sqrt{a}\times\sqrt{b} = \sqrt{ab} ...Rule 2
    So, using these rules, we can say:
    3\sqrt2 =\sqrt3\sqrt3\sqrt2, using Rule 1
    =\sqrt{3\times3\times2}, using Rule 2, twice

    =\sqrt{18}
    Here are another couple of examples:
    (1) 5\sqrt3=\sqrt5\sqrt5\sqrt3
    =\sqrt{5\times5\times3}

    =\sqrt{75}
    (2) \sqrt8 + \sqrt2 = \sqrt{2\times2\times2} + \sqrt2
    =2\sqrt2+1\sqrt2

    =3\sqrt2

    =\sqrt{18}
    Grandad
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  3. #3
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    Quote Originally Posted by hovermet View Post
    I don't understand how 3√2 = to √18.. and how to get rid of the root to become 3 x 2. Can anyone show me a few more examples also?

    Thank You
    3\sqrt{2}= \sqrt{3^2}\sqrt{2}= \sqrt{9}\sqrt{2}= \sqrt{9(2)}= \sqrt{18}. I don't know what you mean by "get rid of the root to become 3 x 2". You can't- 3\sqrt{2} and 3x2 are not equal and you can't just "make" them equal.
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