Question

20. Сократите дробь.​

Answer 1

Ответ:

$1) \frac{ \sqrt{6} - \sqrt{2} }{ \sqrt{8} } = \frac{ \sqrt{3} \times \sqrt{2} - \sqrt{2} }{2 \sqrt{2} } = \frac{ \sqrt{3} - 1}{2}$

$2) \frac{ \sqrt{6} + \sqrt{15} }{ \sqrt{8} + \sqrt{20} } = \frac{ \sqrt{3} \times \sqrt{2} + \sqrt{3} \times \sqrt{5} }{2 \sqrt{2} + 2 \sqrt{5} } = \frac{ \sqrt{3} ( \sqrt{2} + \sqrt{5} )}{2( \sqrt{2} + \sqrt{5} )} = \frac{ \sqrt{3} }{2}$

$3) \frac{10 - 2 \sqrt{5} }{ \sqrt{20} - 2 } = \frac{2(5 - \sqrt{5}) }{2( \sqrt{5} - 1)} = \frac{2 \sqrt{5}( \sqrt{5} - 1) }{2( \sqrt{5} - 1) } = \frac{2 \sqrt{5} }{2} = \sqrt{5}$

$4) \frac{4 + 2 \sqrt{2} }{ \sqrt{8} + 2 } = \frac{2 \sqrt{2} ( \sqrt{2} + 1)}{2( \sqrt{2} + 1) } = \frac{2 \sqrt{2} }{2} = \sqrt{2}$