Question

Tính P = √(13-√(160)) - √(53+4√(90))

Answer 1

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

.....\(=\sqrt{13-4\sqrt{10}}-\sqrt{53+12\sqrt{10}}\)

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

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

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

.....\(=-4\sqrt{5}\)