Question

if √2 =1.414 and √3 =1.732 the find the value of √2 +√3 / √3 -√2

Answer 1

Hey friend,
Here is the answer you were looking for:
$\frac{ \sqrt{2} + \sqrt{3} }{ \sqrt{3} - \sqrt{2} }$

On rationalizing the denominator we get,

$= \frac{ \sqrt{2} + \sqrt{3} }{ \sqrt{3} - \sqrt{2} } \times \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} + \sqrt{2} }$

Using the identity :

$( x + y)(x - y) = {x}^{2} - {y}^{2}$

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

Splitting √6 we get

= 5 + 2 × √2 × √3

= 5 + 2 × 1.414 × 1.732

= 5 + 4.898

= 9.898

Hope this helps!!

If you have any doubt regarding to my answer, feel free to ask in the comment section or inbox me if needed.

@Mahak24

Thanks...
☺☺