Question

<br />$\sqrt{2} + \sqrt{3} \div \sqrt{2} - 2 \sqrt{3} \:$<br />​

Answer 1

Answer:

1.319.

Step-by-step explanation:

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

Rationalizing the denominator we get:

$= \frac{ \sqrt{2} + \sqrt{3} }{ \sqrt{2} - 2 \sqrt{3} } \times \frac{ \sqrt{2} + 2 \sqrt{3} }{ \sqrt{2} + 2 \sqrt{3} } \\ \\ = \frac{ \sqrt{2}( \sqrt{2} + 2 \sqrt{3} ) + \sqrt{3}( \sqrt{2} + 2 \sqrt{3} ) }{ {( \sqrt{2} )}^{2} - {(2 \sqrt{3} )}^{2} } \\ \\ = \frac{2 + 2 \sqrt{6} + \sqrt{6} + 6 }{2 - 12} \\ \\ = \frac{8 + 3 \sqrt{6} }{ - 10} \\ \\ = \frac{ - 8 - 3 \sqrt{6} }{10} \: \\ \\ \bf we \: know \: that \: \sqrt{3} = 1.732 \\ \\ = \frac{ - 8 - 3(1.732)}{10} \\ \\ = \frac{ - 8 - 5.196}{10} \\ \\ = \frac{ - 13.196}{10} \\ \\ \bf = - 1.319$