Question

[Killer world]

Tính: a)  \(\frac{\sqrt{27\left(1-\sqrt{3}\right)^4}}{3\sqrt{15}}\)

b) \(\frac{12\sqrt{10}-8\sqrt{200}+7\sqrt{450}}{\sqrt{10}}\)

c) \(\frac{\sqrt{x}}{\sqrt{y}}\). \(\sqrt{x.\sqrt{y}}\)

Answer 1

[Hoàng Thanh Tuấn]

1. \(\frac{\sqrt{27\left(1-\sqrt{3}\right)^4}}{3\sqrt{15}}=\frac{\sqrt{3.3^2\left(1-\sqrt{3}\right)^4}}{3\sqrt{15}}=\frac{3\left(1-\sqrt{3}\right)^2}{3\sqrt{15}}=\frac{1-2\sqrt{3}+3}{\sqrt{15}}=\frac{4-2\sqrt{3}}{\sqrt{15}}\)
2. \(=\frac{\sqrt{10}\left(12-8\sqrt{2}+7.15\sqrt{2}\right)}{\sqrt{10}}=12+97\sqrt{2}\)
3. \(=\sqrt{\frac{x.x\sqrt{y}}{y}}=\sqrt{\frac{x^2}{\sqrt{y}}}=\frac{|x|}{\sqrt[4]{y}}\)