Question

Root 3 minus root 2 divided by root 3 + root 2​

Answer 1

Answer:

$5 - 2 \sqrt{6}$

Step-by-step explanation:

Perhaps you are interested in rationalising the denominator of the given problem. Let's do it.

$\frac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3} + \sqrt{2} } \\ \\ multiplying \: numerator \: and \: denominator \: \\ by \: (\sqrt{3} - \sqrt{2}) \\ \\ \frac{( \sqrt{3} - \sqrt{2} ) }{ (\sqrt{3} + \sqrt{2} )} \times \frac{ (\sqrt{3} - \sqrt{2} )}{ (\sqrt{3} - \sqrt{2} )} \\ \\ = \frac{{( \sqrt{3} - \sqrt{2} )}^{2} }{ { (\sqrt{3} })^{2} - {( \sqrt{2} })^{2} } \\ \\ = \frac{ { (\sqrt{3} )}^{2} + { (\sqrt{2} )}^{2} - 2 \sqrt{3 \times 2} }{3 - 2} \\ \\ = \frac{3 + 2 - 2 \sqrt{6} }{1} \\ \\ = 5 - 2 \sqrt{6}$