Obliczenia :
[tex] \sqrt{5 - 2 \sqrt{6} } \times \sqrt{5 + 2 \sqrt{6} } = \\ \\ = \sqrt{(5 - 2 \sqrt{6})(5 + 2 \sqrt{6}) } = \\ \\ = \sqrt{ {5}^{2} - {(2 \sqrt{6} )}^{2} } = \sqrt{25 - 24} = \sqrt{1} = 1[/tex]
Odpowiedź:
[tex]\sqrt{5-2\sqrt{6}}\times\sqrt{5+2\sqrt{6}} =\sqrt{(5-2\sqrt{6})\times(5+2\sqrt{6}} =\sqrt{5^{2}-(2\sqrt{6})^{2}}} = \sqrt{25-4\times6} =\\\\= \sqrt{25-24} = \sqrt{1} = 1[/tex]
Szczegółowe wyjaśnienie:
[tex](a-b)(a+b) = a^{2}-b^{2}[/tex]