Question

$\sqrt{5} + \sqrt{2} \div \sqrt{5} - \sqrt{2}$
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Answer 1

Step-by-step explanation:

$\\ \tt{:}\Rrightarrow \frac{ \sqrt{5} + \sqrt{2} }{ \sqrt{5} - \sqrt{2} } \\ \\ \tt{:}\Rrightarrow \frac{( \sqrt{5} + \sqrt{2})( \sqrt{5} - \sqrt{2} )}{( \sqrt{5} - \sqrt{2} )( \sqrt{5} - \sqrt{2}) } \\ \\ \tt{:}\Rrightarrow \frac{ {( \sqrt{5} )}^{2} - (\sqrt{2}) {}^{2} }{ {( \sqrt{5} - \sqrt{2}) }^{2} } \\ \\ \tt{:}\Rrightarrow \frac{5 - 2}{ {( \sqrt{5}) }^{2} - 2 \sqrt{5} \sqrt{2} + (\sqrt{2} ) {}^{2} }\\ \\ \tt{:}\Rrightarrow \frac{3}{5 - 2 \sqrt{5} \sqrt{2} + 2 } \\ \\ \tt{:}\Rrightarrow \frac{3}{3 - 2 \sqrt{5} \sqrt{2} } \\ \\ \tt{:}\Rrightarrow \frac{3}{3 - 2 \sqrt{5 \times 2} } \\ \\ \tt{:}\Rrightarrow \frac{3}{3 - 2 \sqrt{10} } \\ \\ \tt{:}\Rrightarrow \frac{3}{3-2(3.1)} \\ \\ \tt{:}\Rrightarrow \frac{3}{3-6.2}\\ \\ \tt{:}\Rrightarrow \frac{3}{-2.8}\\ \\ \tt{:}\Rrightarrow -1.07 \\ \\ \tt{:}\Rrightarrow -1(Approximately)$