Question

20 баллов за решение:
$\sqrt{8 - \sqrt{15} }$
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Answer 1

Ответ:

$\displaystyle\sqrt{\frac{15}{2}} - \sqrt{\frac{1}{2}}$

Пошаговое объяснение:

$\displaystyle{\sqrt{8-\sqrt{15}} = \sqrt{\frac{1}{2}-2 * \sqrt{\frac{1}{2}}\sqrt{\frac{15}{2}} + \frac{15}{2}}} = \sqrt{\left(\sqrt{\frac{1}{2}} - \sqrt{\frac{15}{2}}\right)^2} = \left| \sqrt{\frac{1}{2}} - \sqrt{\frac{15}{2}} \right| = \sqrt{\frac{15}{2}} - \sqrt{\frac{1}{2}}$

Answer 2

$\sqrt{8-\sqrt{15}}=\frac{\sqrt{16-2\sqrt{15}}}{\sqrt{2}}=\frac{\sqrt{(\sqrt{15})^2-2\sqrt{15}\cdot 1+1^2}}{\sqrt{2}}=\frac{\sqrt{(\sqrt{15}-1)^2}}{\sqrt{2}}= \frac{|\sqrt{15}-1|}{\sqrt{2}}}=$

$\frac{\sqrt{2}}{2}\cdot (\sqrt{15}-1)=\frac{\sqrt{30}-\sqrt{2}}{2}$