Question

$\frac{ \sqrt{2} }{ \sqrt{5 + } \sqrt{3} }$
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Answer 1

Answer:

$\frac{ \sqrt{10} - \sqrt{15} }{2}$

Step-by-step explanation:

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

Since

$(a - b)(a + b) = {a}^{2} - {b}^{2}$

$\frac{ \sqrt{10} - \sqrt{15} }{( \sqrt{5})^{2} - ( \sqrt{3}) ^{2} }$

$\frac{ \sqrt{10} - \sqrt{15} }{5 - 3}$

$\frac{ \sqrt{10} - \sqrt{15} }{2}$