3 root 2 - 2 root 3 / 3 root 2 + 2 root 3

Question

It is the question of rational numbers in which we have to do rationalize 

Answer 1

Ansh, I’m going to guess that the original problem was something like 

(3√2 - 2√3) / (3√2 + 2√3)

 

To get rid of roots in a denominator, it can be useful to use the formula for difference of squares.

x² - y² = ( x+y)(x-y)

Our Denominator is of the form (x+y), so multiply both numerator and denominator by (x-y), or (3√2 - 2√3).

 

so the new numerator is 

(3√2 - 2√3)²

and then the new denominator is

(3√2)^{2 -} (2√3)² 

Lets simplify the denominator

9*2 - 4*3 = 18-12 = 6

 

now multiply out the numerator

 

(3√2)² -  2*3√2*2√3) + (2√3)²=

9*2 -12√6 + 4*3 =

18+12 - 12√6 =30-12√6

Finally put the numerator in top of the denominator again 

(30-12√6) / 6 =

5 - 2√6