Question

2/√5-√3-3/√3+√2-2/√5-√2​

Answer 1

Answer:

0.16237638343103858503622

Answer 2

Step-by-step explanation:

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

Let us find the value of each term,

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

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

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

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

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

$= \frac{ \sqrt{5} }{3} - \frac{7 \sqrt{2} }{3} - 2 \sqrt{3}$

$= \frac{ \sqrt{5} - 7 \sqrt{2} - 6 \sqrt{3} }{3}$