Question

Cum se rezolva $\sqrt{5- 2\sqrt{6} }$ ca sa dea $\sqrt{3}- \sqrt{2}$

Answer 1

           
$\sqrt{5- 2\sqrt{6}} = \\ = \sqrt{3- 2\sqrt{6}+2}= \\ =\sqrt{ ( \sqrt{3} )^{2} - 2\sqrt{3}\sqrt{2}+(\sqrt{2} )^{2}}= \\ = \sqrt{ ( \sqrt{3}- \sqrt{2} )^{2}} = \sqrt{3}- \sqrt{2}$


Am folosit formulele:
a = (√a)²
si 
a² - 2ab + b² = (a - b)²
si
√(a - b)²  = a - b

Answer 2

Raspuns:
[tex] \sqrt{5- 2\sqrt{6}} = \sqrt{3} - \sqrt{2} \\= \sqrt{3- 2\sqrt{6}+2} \\ =\sqrt{ ( \sqrt{3} )^{2} - 2\sqrt{3}\sqrt{2}+(\sqrt{2} )^{2}} \\ = \sqrt{ ( \sqrt{3}- \sqrt{2} )^{2}} \\= \sqrt{3}- \sqrt{2} [/tex]