Question

rationalize 3 / (√3-√2)+√5
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Answer 1

Answer:

Step-by-step explanation:

This is a very good question!

If it were simply 1√a+√b, we would use the conjugate,

and we would multiply by √a−√b√a−√b.

Let's try something like that and see if it works. (This is what we do with problems of kinds we have not seen before. Try something and see if it works.)

1√2+√3+√5=1√2+(√3+√5)

=1[√2+(√3+√5)][√2−(√3+√5)][√2−(√3+√5)]

=[√2−(√3+√5)][√2+(√3+√5)][√2−(√3+√5)]

=[√2−(√3+√5)]2−(√3+√5)2

=[√2−(√3+√5)]2−(3+2√15+5)

=[√2−(√3+√5)]−6−2√15

Did that help? (Yes, it did. We now have a more familiar looking problem.

=[√2−(√3+√5)][−6+2√15][−6−2√15][−6+2√15]

=[√2−(√3+√5)][−6+2√15]36−4(15)

=[√2−(√3+√5)][−6+2√15]−24

=[√2−(√3+√5)][3−√15]12

Multiply the numerator if you like, to get:

=[√2−√3−√5][3−√15]12

=[√2−√3−√5][3−√15]12

=3√2−3√3−3√5−√30+√45+√7512

=3√2−3√3−3√5−√30+3√5+5√312

=3√2+2√3−√3012

I hope it is clear for you. If you have any doubt please ask me.