Question

Rút gọn

a)\(\sqrt{8+\sqrt{7}}-\sqrt{8-\sqrt{7}}\)

b)\(\sqrt{3-\sqrt{5}}\cdot\left(\sqrt{10}-\sqrt{2}\right)\cdot\left(8+\sqrt{5}\right)\)

Answer 1

\(\sqrt{3-\sqrt{5}}\left(\sqrt{10}-\sqrt{2}\right)\left(8+\sqrt{5}\right)\\ =\sqrt{3-\sqrt{5}}.\sqrt{2}\left(\sqrt{5}-1\right)\left(8+\sqrt{5}\right)\\ =\sqrt{6-2\sqrt{5}}\left(\sqrt{5}-1\right)\left(8+\sqrt{5}\right)\\ =\sqrt{\left(\sqrt{5}-1\right)^2}\left(\sqrt{5}-1\right)\left(8+\sqrt{5}\right)\\ =\left(\sqrt{5}-1\right)^2\left(8+\sqrt{5}\right)\\ =\left(6-2\sqrt{5}\right)\left(8+\sqrt{5}\right)\)

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