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Math Help - root question

  1. #1
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    root question

    Can anyone explain the following:

    A)
    \frac{\sqrt{2}}{2}=\frac{1}{\sqrt{2}}

    and the ratio/proportion:
    B)
    1 : \frac{1}{\sqrt{2}} = \sqrt{2} : 1



    thanks in advance

    How on earth is A) true?
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  2. #2
    Senior Member MacstersUndead's Avatar
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    A) You can rewrite this equation with exponents

    Consider that the square root of 2 = 2^(1/2)
    now with the exponent law of division, can you finish?
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  3. #3
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    e^(i*pi)'s Avatar
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    \frac{\sqrt2}{\sqrt2} = 1

    And as we know multiplying by 1 does not affect the value of a number.

    \frac{1}{\sqrt2} \times \frac{\sqrt2}{\sqrt2} = \frac{\sqrt2}{2}

    You'll come across this more when it comes to Rationalising the Denominator
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  4. #4
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    Grandad's Avatar
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    Hello portia
    Quote Originally Posted by portia View Post
    Can anyone explain the following:

    A)
    \frac{\sqrt{2}}{2}=\frac{1}{\sqrt{2}}

    and the ratio/proportion:
    B)
    1 : \frac{1}{\sqrt{2}} = \sqrt{2} : 1



    thanks in advance

    How on earth is A) true?
    The only things you really need to understand here are:

    • \sqrt2\times\sqrt2 = 2 (because that's what a square root is)


    • how to 'cancel' a fraction

    Then it works like this:

    \frac{\sqrt2}{\color{red}2}=\frac{\sqrt2}{\color{r  ed}\sqrt2\times\sqrt2}

    ... and 'cancel' in the usual way:

    \frac{\sqrt2}{2}=\frac{\color{blue}\sqrt2}{\color{  blue}\sqrt2\color{black}\times\sqrt2}=\frac{1}{\sq  rt2}

    For B, you also need to understand that ratios work exactly like fractions: you can 'cancel' (i.e. divide each number in the ratio by the same thing) or you can 'un-cancel' (if there is such a word) by multiplying each number in the ratio by the same thing.

    So starting with 1:\frac{1}{\sqrt2}, multiply each number by \sqrt2:

    1:\frac{1}{\sqrt2}=1\color{red}\times\sqrt2\color{  black}:\frac{1}{\sqrt2}\color{red}\times \sqrt2

    = \sqrt2:\frac{\sqrt2}{\sqrt2}

    =\sqrt2:1

    Grandad
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  5. #5
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    Thanks, I understand it now. After substracting the exponents we're left with 2^(-1/2) which gives 1 over the square root of 2.

    My maths skills are VERY rusty.

    What about the ration question?

    edit: sorry, I only saw the first reply.
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  6. #6
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    Thanks guys, I get it now
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