Question

Tính  \(\sqrt{13-\sqrt{160}}-\sqrt{53+4\sqrt{90}}\)

Answer 1

\(\sqrt{13-4\sqrt{10}}-\sqrt{53+4\sqrt{90}}\)

\(=\sqrt{\left(2\sqrt{2}\right)^2-2.2\sqrt{2}\sqrt{5}+\left(\sqrt{5}\right)^2}-\sqrt{\left(2\sqrt{2}\right)^2+2.2\sqrt{2}.3.\sqrt{5}+\left(3\sqrt{5}\right)^2}\)

\(=\sqrt{\left(2\sqrt{2}-\sqrt{5}\right)^2}-\sqrt{\left(2\sqrt{2}+3\sqrt{5}\right)^2}\)

= \(\) \(2\sqrt{2}-\sqrt{5}-2\sqrt{2}-3\sqrt{5}=-4\sqrt{5}\)

Answer 2

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