Question

Решите, . корень из разности 2 и корня из 3.

Answer 1

$\sqrt{2 - \sqrt{3}}= \sqrt{\frac{1 - 2\sqrt{3}+(\sqrt{3})^2}{2}}=\sqrt{\frac{(1-\sqrt{3})^2}{2}}=\frac{\sqrt{3}-1}{\sqrt{2}}= \frac{(\sqrt{3}-1) \ \cdot \sqrt{2}}{\sqrt{2} \ \cdot \sqrt{2}}= \frac{\sqrt{6}- \sqrt{2}}{2}$

Answer 2

$\sqrt{2- \sqrt{3} } = \sqrt{2(2- \sqrt{3})/2 } = \sqrt{(4-2 \sqrt{3})/2 } = \sqrt{( \sqrt{3}-1)^2/2 }=$$( \sqrt{3}-1)/ \sqrt{2} = \sqrt{2} ( \sqrt{3} -1)/2$