# Rationalize the numerator

1. Dec 1, 2008

### elie_girl

Rationalize the numerator

sqrt(5)+3/-4sqrt(7)

The answer I got for this was -(sqrt(5)+3*sqrt(7)/28) and it marked it as wrong.

2. Dec 1, 2008

### horatio89

I think you rationalised the denominator instead of the numerator...

3. Dec 1, 2008

### elie_girl

How do I rationalize the numerator?

4. Dec 1, 2008

### horatio89

Almost the exact same way you normally rationalise the denominator. The difference is that this time you multiply both top and bottom with the conjugate of the numerator.

5. Dec 1, 2008

### Georgepowell

That should be right, although I do make a lot of mistakes usually :p

1. You multiply the top and the bottom by the same value that you are trying to rationalise, except the non-surd part of the expression needs to be turned from a positive to negative, this way the two square roots create an integer, and the surd disappears.

2. you simplify :)

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6. Dec 1, 2008

### elie_girl

So then would the answer be (sqrt(5)+3sqrt(7))/14 ?

7. Dec 1, 2008

### Georgepowell

No, sorry.

Rationalise means get rid of all the square roots. And Numerator means the top of the fraction, and you have not got rid of the square roots on the top of the fraction

You get rid of a square root by squaring it, then it turns into an integer.

If you want to rationalise [sqrt(A) + B] then you multiply it by [sqrt(A) - B]

note the negative 'B'

When you are doing this with a fraction, multiply the top and the bottom by the same value (so you can keep the overall value the same).

I did this step-by-step in the picture I attached with my last post, it ended with the final answer as well.

Do you have any more questions? I'm glad to help.

8. Dec 2, 2008

### elie_girl

Oh ok, I think I get it now. Thanks very much!

9. Jan 22, 2010

### charmaine

Please rationalize root (x plus 4) - 2 divided by x