Question

Rationalise 7/3√3-2√2

Answer 1

7 /  (3√3  - 2 √2 )  
multiply both numerator and denominator by (3√3 + 2√2)
we choose +2√2 as, in the given expression, we have -2√2.

             7 (3√3 + 2√2)                
=  ---------------------------------      =
       (3√3 + 2√2) (3√3 - 2√2)           

   21 √3  + 14 √2            21 √3 + 14 √2
  ---------------------    =    --------------------
  3² 3 - 2² 2                          27 - 8

= (21 √3 + 14√2) / 19

Answer 2

$Use:(a-b)(a+b)=a^2-b^2$


$\frac{7}{3\sqrt3-2\sqrt2}=\frac{7}{3\sqrt3-2\sqrt2}\times\frac{3\sqrt3+2\sqrt2}{3\sqrt3+2\sqrt2}=\frac{7(3\sqrt3+2\sqrt2)}{(3\sqrt3-2\sqrt2)(3\sqrt3+2\sqrt2)}\\\\=\frac{7(3\sqrt3-2\sqrt2)}{(3\sqrt3)^2-(2\sqrt2)^2}=\frac{7(3\sqrt3-2\sqrt2)}{3^2(\sqrt3)^2-2^2(\sqrt2)^2}=\frac{7(3\sqrt3-2\sqrt2)}{9(3)-4(2)}\\\\=\frac{7(3\sqrt3-2\sqrt2)}{27-8}=\frac{7(3\sqrt3-2\sqrt2)}{19}=\frac{21\sqrt3-14\sqrt2}{19}$