Question

Rezolvați complet exerciţiile

Answer 1

$\star) \frac{ \sqrt{15} - \sqrt{6} }{ \sqrt{3} } = \frac{ \sqrt{3} ( \sqrt{15} - \sqrt{6} ) }{3} = \frac{ \sqrt{45} - \sqrt{18} }{3}$

$= \frac{3 \sqrt{5} - 3 \sqrt{2} }{3} = \frac{3( \sqrt{5} - \sqrt{2}) }{3} = \sqrt{5} - \sqrt{2}$

$\star) \frac{ \sqrt{42} - \sqrt{18} }{ \sqrt{6} } = \frac{ \sqrt{6} ( \sqrt{42} - \sqrt{18} ) }{6} = \frac{ \sqrt{252} - \sqrt{108} }{6}$

$= \frac{6 \sqrt{7} - 6 \sqrt{3} }{6} = \frac{6( \sqrt{7} - \sqrt{3} )}{6} = \sqrt{7} - \sqrt{3}$

$\star) \frac{2 \sqrt{15} - 3 \sqrt{10} }{ \sqrt{5} } = \frac{ \sqrt{ {2}^{2} \times 15} - \sqrt{ {3}^{2} \times 10 } }{ \sqrt{5} }$

$= \frac{ \sqrt{4 \times 15} - \sqrt{9 \times 10} }{ \sqrt{5} } = \frac{ \sqrt{60} - \sqrt{90} }{ \sqrt{5} }$

$= \frac{ \sqrt{5}( \sqrt{60} - \sqrt{90}) }{5} = \frac{ \sqrt{300} - \sqrt{450} }{5}$

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

$\star) \frac{3 \sqrt{28} - \sqrt{21} }{ \sqrt{7} } = \frac{ \sqrt{ {3}^{2} \times 28 } - \sqrt{21} }{ \sqrt{7} }$

$= \frac{ \sqrt{9 \times 28} - \sqrt{21} }{ \sqrt{7} } = \frac{ \sqrt{252} - \sqrt{21} }{ \sqrt{7} }$

$= \frac{ \sqrt{7} ( \sqrt{252} - \sqrt{21}) }{7} = \frac{ \sqrt{1764} - \sqrt{147} }{7}$

$= \frac{42 - 7 \sqrt{3} }{7} = \frac{7(6 - \sqrt{3}) }{7} = 6 - \sqrt{3}$