Question

избавьтесь от внешнего корня $\sqrt{5-\sqrt{24} }$

Answer 1

Ответ:

Объяснение:

• $(\sqrt{a}-\sqrt{b} )^2=a^2-2\sqrt{ab} +b^2$

• $\sqrt{(\sqrt{a}-\sqrt{b} )^2}=|\sqrt{a}-\sqrt{b}|$

$\displastyle \sqrt{5-\sqrt{24} } =\sqrt{5-2\sqrt{6} } = \sqrt{\underbrace{3+2}_5-2\underbrace{\sqrt{3}\cdot \sqrt{2} }_{\sqrt{6} } } =\\\\\\ \sqrt{\underbrace{3}_{a^2}-2\underbrace{\sqrt{3}\sqrt{2}}_{ab}+\underbrace{2 }_{b^2} } =\sqrt{(\sqrt{3}-\sqrt{2} )^2 } =|\sqrt{3}-\sqrt{2} |=\boxed{\sqrt{3}-\sqrt{2} }$

Answer 2

Ответ:

$\displaystyle \sqrt{3} - \sqrt{2}$

Объяснение:

$\displaystyle \sqrt{5 - \sqrt{24}} = \sqrt{5 - 2\sqrt{6}} = \sqrt{\sqrt{3}^2-2*\sqrt{3}*\sqrt{2} + \sqrt{2}^2} = \sqrt{(\sqrt{3} - \sqrt{2})^2} = \\= \left| \sqrt{3} - \sqrt{2} \right| = \sqrt{3} - \sqrt{2}$