Question

Срочно! помогите пожалуйста, умоляю ​

Answer 1

Ответ:

Пошаговое объяснение:

а) $\frac{\sqrt{10} - \sqrt{5}}{\sqrt{5}} = \frac{\sqrt{2 * 5} - \sqrt{5} }{\sqrt{5}} = \frac{\sqrt{2} * \sqrt{5} - \sqrt{5} }{\sqrt{5}} = \frac{\sqrt{5} (\sqrt{2} - 1)}{\sqrt{5} } = \sqrt{2} -1$

б) $\frac{\sqrt{6} - \sqrt{18}}{\sqrt{6}} = \frac{\sqrt{6} - \sqrt{6 * 3} }{\sqrt{6}} = \frac{\sqrt{6} - \sqrt{6}* \sqrt{3} }{\sqrt{6}} = \frac{\sqrt{6} (1 - \sqrt{3})}{\sqrt{6} } = 1 - \sqrt{3}$

в) $\frac{\sqrt{21} + \sqrt{14}}{\sqrt{7}} = \frac{\sqrt{7 * 3} + \sqrt{7 * 2} }{\sqrt{7}} = \frac{\sqrt{7} * \sqrt{3} + \sqrt{7}* \sqrt{2} }{\sqrt{7}} = \frac{\sqrt{7} (\sqrt{3} + \sqrt{2})}{\sqrt{7} } = \sqrt{3} + \sqrt{2}$

г) $\frac{\sqrt{15} - 5}{\sqrt{6} - \sqrt{10} } = \frac{\sqrt{5 * 3} - \sqrt{5}*\sqrt{5} }{\sqrt{2*3} - \sqrt{5*2} } = \frac{\sqrt{5} * \sqrt{3} - \sqrt{5}* \sqrt{5} }{\sqrt{2}*\sqrt{3} -\sqrt{2}*\sqrt{5} } = \frac{\sqrt{5} (\sqrt{3} - \sqrt{5})}{\sqrt{2}(\sqrt{3} -\sqrt{5}) } = \frac{\sqrt{5} }{\sqrt{2}}$