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19 May, 15:47

What is square root 10 over square root 3 in simplest radical form

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  1. 19 May, 16:21
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    I'll give you a few examples of a square root over a square root first, so you'll understand how I got the answer:

    1. √a / √b = √ab / b

    2. √2 / √3 = √2*3 / 3 = √6 / 3

    3. 1 / √a = √a / a

    4. √3 / √7 = √21 / 7

    I think you get how it works now.

    Now lets solve the question.

    √10 / √3

    can also be written as √10 * 1/√3

    1/√3 simplified is √3/3

    So, √10 / √3 = √10 * √3/3

    = √10*√3 / 3

    = √30 / 3

    Factor 30 (2*3*5) and make sure there are no pairs of factors that are the same. (for example: two 2's or two 4's)

    If there are any pairs of factors, then take them outside the square root.

    ex: √20 = √2*2*5 = 2√5

    That was the long way to solve it, but there is a trick:

    Remember what √a / √b equals?

    It equals √a*b / b.

    This means √10 / √3 is simply just √30 / 3.

    Then all you need to do is make sure the number inside the radical has no pairs of factors then you are good to go.
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