Упростите выражение:
1) $\sqrt{8 - 2\sqrt{7}}$;
2) $\sqrt{5 - 2\sqrt{6}}$;
3) $\sqrt{12 - 6\sqrt{3}}$;
4) $\sqrt{38 - 12\sqrt{2}}$.
$\sqrt{8 - 2\sqrt{7}} = \sqrt{1 + 7 - 2\sqrt{7}} = \sqrt{1^2 - 2 * 1 * \sqrt{7} + (\sqrt{7})^2} = \sqrt{(1 - \sqrt{7})^2} = |1 - \sqrt{7}| = -1 + \sqrt{7} = \sqrt{7} - 1$
$\sqrt{5 - 2\sqrt{6}} = \sqrt{3 + 2 - 2\sqrt{6}} = \sqrt{(\sqrt{3})^2 - 2\sqrt{3 * 2} + (\sqrt{2})^2} = \sqrt{(\sqrt{3} - \sqrt{2})^2} = |\sqrt{3} - \sqrt{2}| = \sqrt{3} - \sqrt{2}$
$\sqrt{12 - 6\sqrt{3}} = \sqrt{9 + 3 - 6\sqrt{3}} = \sqrt{3^2 - 2 * 3 * \sqrt{3} + (\sqrt{3})^2} = \sqrt{(3 - \sqrt{3})^2} = |3 - \sqrt{3}| = 3 - \sqrt{3}$
$\sqrt{38 - 12\sqrt{2}} = \sqrt{36 + 2 - 12\sqrt{2}} = \sqrt{6^2 - 2 * 6 * \sqrt{2} + (\sqrt{2})^2} = \sqrt{(6 - \sqrt{2})^2} = |6 - \sqrt{2}| = 6 - \sqrt{2}$
Пожауйста, оцените решение
