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Thread: 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: $\displaystyle \sqrt{a}\times\sqrt{a} = a$ ...Rule 1

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

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

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

    $\displaystyle =3\sqrt2$

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