Rationalize the denominator???

Question

I got a really hard rationaizing question...

question...

1/(1+√3-√5)

answer

(7 + 3√3 + √5 + 2√15) / 11

I just dont know how to show the work for this, its like above anything we have even touched or even thought of learning..

thanks..

I need the work, if you dont show work in the answer, dont even tell me about it!

Answer 1

Try this.

Look at the denominator as (1 + sqrt 3) - sqrt 5.  Now multiply the numerator and denominator by

(1 + sqrt 3) + sqrt 5.  This will eliminate the sqrt 5 in the denominator.  I get 2sqrt 3 -1 for the new denominator.  Then you can multiply numerator and denominator by

2sqrt 3 + 1 to finish off the rationalization.  If you do everything correctly, you will get the answer above.

Answer 2

Have you tried multiplying the denominator with its conjugate?

1

----------------

(1+√3-√5)

Treat the square root of 3 and square root of 5 as one factor.

Treat 1 as one factor.

Multiply numerator and denominator by 1 minus (the square root of 3 subtract by the square root of 5)

I believe the reason why this is more difficult because when you have to rationalize the denominator, you must multiply √3-√5 with √3-√5, which turns out to be 3-2√3√5+5 = 3-2√15+5.

So, the entire denominator is 1+3-2√15+5.

And, the entire numerator is (1-√3-√5).

Now, you have to simplify.

The point of rationalizing the denominator is removing the radical sign, but since we have calculators these days, it's not that important anymore, because our trusty calculators can do anything.