Question

Rationalize the Denominator...
the square route of 13 minus the square route of 2 over the square route of 2 plus the square route of 13. Help...

Answer 1

here;s a example to solve ur's ques...
There is just one square root in the denominator, so this is case 1. So to get rid of it we just multiply top and bottom by it. The square root of 3 times the square root of 3 is 3 simply from the meaning of square root, you don't have to write it first as the square root of 9. Remember that the square root of 3 means the number you can square, that is multiply by itself, to get 3, so if you squared it and didn't get 3 it wouldn't be the square root of 3. So by multiplying the top and the bottom by the square root of 3 we get rid of the square root in the bottom. In punishment for this the top got more complicated, and in fact the whole thing does in fact look more complicated after this 'simplification', but many times, like for example when you are adding and need to find common denominators, this sacrifice is worth it, because simplicity is more important in denominators than in numerators.

Answer 2

Actually Rohangrr...there is a sq. rt of 2 + sq. rt. of 13 in the denominator...2 square routes, not one.

Answer 3

To rationalize a fraction, we can first multiply the conjugate of the denominator to both numerator and denominator.
(sqrt (13)-sqrt(2))/(sqrt(2)+sqrt(13)
=(sqrt(13)-sqrt(2))(sqrt(2)-sqrt(13)) / (sqrt(2)+sqrt(13))(sqrt(2)-sqrt13))
=(sqrt(13)-sqrt(2))(sqrt(2)-sqrt(13))/ (2-13)
=-2+2sqrt(13)sqrt(2)-13 /-11
=-15+2sqrt(13)sqrt(2) / -11