Question

Rationalize the denominator of √3+√2\ 5+√2 ​

Answer 1

`( 5 \sqrt3 \ + \ 5 \sqrt2 \ - \ \sqrt6 \ - \ 2)/(23)`

Explanation:

`(\sqrt3 \ + \ \sqrt2 )/(5 \ + \ \sqrt2 ) \\\\=(\sqrt3 \ + \ \sqrt2 )/(5 \ + \ \sqrt2 ) * (5 \ - \ \sqrt2 )/(5 \ - \ \sqrt2 ) \\\\=(( \sqrt3 \ + \ \sqrt2)(5 \ - \ \sqrt2))/((5 \ + \ \sqrt2)( 5 \ - \ \sqrt 2 ))\\\\=(( \sqrt3 \ + \ \sqrt2)(5 \ - \ \sqrt2))/((5 \ + \ \sqrt2)( 5 \ - \ \sqrt 2 ))\\\\=(5 \sqrt3 \ + \ 5\sqrt 2 \ - \ √( 3* 2 ) \ - \ √(2 * 2))/((5)^2 \ - \ (\sqrt2)^2)\\\\= ( 5 \sqrt3 \ + \ 5 \sqrt2 \ - \ \sqrt6 \ - \ 2)/(25 - 2)\\\\`

`= ( 5 \sqrt3 \ + \ 5 \sqrt2 \ - \ \sqrt6 \ - \ 2)/(23)`