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Math Help - rationalising denominators

  1. #1
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    rationalising denominators

    hi, i need to rationalise the denominator of this,  \frac{1}{2\sqrt{3}}

    how would i work this out?
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  2. #2
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    Smile

    Here's one I prepared earlier.

    Consider

     \frac{1}{4\sqrt{5}}

    Let's times it by 1 because that won't change anything

     \frac{1}{4\sqrt{5}}\times 1

    But 1 comes in many forms I.e \frac{a}{a}=1, a\neq 0

    So lets make it the following

     \frac{1}{4\sqrt{5}}\times \frac{\sqrt{5}}{\sqrt{5}}

    I did this because \sqrt{a}\times \sqrt{a}= a

    Now we have

     \frac{1\times \sqrt{5}}{4\sqrt{5}\times \sqrt{5}}

     \frac{\sqrt{5}}{4\times 5}

    We have no radical in the denominator so we are finished.

    Apply this method to your problem.
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  3. #3
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    Quote Originally Posted by pickslides View Post
    Here's one I prepared earlier.

    Consider

     \frac{1}{4\sqrt{5}}

    Let's times it by 1 because that won't change anything

     \frac{1}{4\sqrt{5}}\times 1

    But 1 comes in many forms I.e \frac{a}{a}=1, a\neq 0

    So lets make it the following

     \frac{1}{4\sqrt{5}}\times \frac{\sqrt{5}}{\sqrt{5}}

    I did this because \sqrt{a}\times \sqrt{a}= a

    Now we have

     \frac{1\times \sqrt{5}}{4\sqrt{5}\times \sqrt{5}}

     \frac{\sqrt{5}}{4\times 5}

    We have no radical in the denominator so we are finished.

    Apply this method to your problem.

     \frac{1}{2\sqrt{3}}\times\frac{\sqrt{3}}{\sqrt{3}}

    but i don't understand how to get the answer
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  4. #4
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    Quote Originally Posted by andyboy179 View Post
     \frac{1}{2\sqrt{3}}\times\frac{\sqrt{3}}{\sqrt{3}}

    but i don't understand how to get the answer
    You have started the problem perfectly, now just follow what I have done in post #2.

    Recall when multiplying fractions \frac{a}{b}\times \frac{c}{d} = \frac{a\times c}{b\times d}
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  5. #5
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    Quote Originally Posted by pickslides View Post
    You have started the problem perfectly, now just follow what I have done in post #2.

    Recall when multiplying fractions \frac{a}{b}\times \frac{c}{d} = \frac{a\times c}{b\times d}
    would the answer to my question be, rationalising denominators-untitled.jpg ?
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  6. #6
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    Yes, yes it is

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  7. #7
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    thank you so much, you'd make a great teacher!!!
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  8. #8
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    oh ye one others thing, is this right? rationalising denominators-untitled.jpg
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  9. #9
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    Quote Originally Posted by andyboy179 View Post
    oh ye one others thing, is this right? Click image for larger version. 

Name:	untitled.jpg 
Views:	9 
Size:	14.4 KB 
ID:	14844
    Yes.
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