Question

Hey man.

Sove this..

$\frac{2 + \sqrt{2} }{ \sqrt{5} - \sqrt{3} }$

Answer 1

Hola Mate!!

Your answer :-

$= > \frac{2 + \sqrt{2} }{ \sqrt{5} - \sqrt{3} } \\ \\ = > \frac{2 + \sqrt{2} }{ \sqrt{5} - \sqrt{3} } \times \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} + \sqrt{3} } \\ \\ = > \frac{2 ( \sqrt{5} + \sqrt{3} ) + \sqrt{2} ( \sqrt{5} + \sqrt{3} ) }{ {( \sqrt{5} )}^{2} - {( \sqrt{3} )}^{2} } \\ \\ = > \frac{2 \sqrt{5} + 2 \sqrt{3} + \sqrt{10} + \sqrt{6} }{5 - 3} \\ \\ = > \frac{2 \sqrt{5 } + 2 \sqrt{3} + \sqrt{10} + \sqrt{6} }{2}$

☆ Hope it helps ☆

Answer 2

ʜᴇʟʟᴏ ᴍᴀᴛᴇ!

( 2 + √2 ) / ( √5 - √3 )

Rationalize

( 2 + √2 ) / ( √5 - √3 ) × ( √5 + √3 ) / ( √5 - √3 )

( 2 + √2 )( √5 + √3 ) / ( 5 - 3 )

( 2√5 + 2√3 + √10 + √6 ) / 2

$\frac{2 \sqrt{5} + 2 \sqrt{3} + \sqrt{10} + \sqrt{6} }{2} \\ \frac{2 \times 2.24 + 2 \times 1.73 + 3.16 + 2.45}{2} \\ \frac{4.48 + 3.46 + 3.16 + 3.45}{2} \\ = \frac{14.55}{2} \: or \: 7.275$

Hope it helps