Bài 56 trang 30 SGK Toán 9 tập 1

Sắp xếp theo thứ tự tăng dần

a) \(3\sqrt{5};\,\,\,2\sqrt{6};\,\,\,\sqrt{29};\,\,\, 4\sqrt{2}\)

b) \(6\sqrt{2};\,\,\, \sqrt{38};\,\,\,3\sqrt{7};\,\,\, 2\sqrt{14}.\)

a) Ta có:

\(\left\{ \matrix{ 3\sqrt 5 = \sqrt {{3^2}.5} = \sqrt {9.5} = \sqrt {45} \hfill \cr 2\sqrt 6 = \sqrt {{2^2}.6} = \sqrt {4.6} = \sqrt {24} \hfill \cr 4\sqrt 2 = \sqrt {{4^2}.2} = \sqrt {16.2} = \sqrt {32} \hfill \cr} \right.\)

Vì: \(24 < 29 < 32 < 45 \Leftrightarrow \sqrt{24}<\sqrt{29}<\sqrt{32}<\sqrt{45}\)

                                        \(\Leftrightarrow 2\sqrt{6}<\sqrt{29}< 4\sqrt{2}< 3\sqrt{5}\)

b)

\(\left\{ \matrix{ 6\sqrt 2 = \sqrt {{6^2}.2} = \sqrt {36.2} = \sqrt {72} \hfill \cr 3\sqrt 7 = \sqrt {{3^2}.7} = \sqrt {9.7} = \sqrt {63} \hfill \cr 2\sqrt {14} = \sqrt {{2^2}.14} = \sqrt {4.14} = \sqrt {56} \hfill \cr} \right.\)

Vì: \(38 < 56 < 63 < 72\Leftrightarrow \sqrt{38}<\sqrt{56}<\sqrt{63}<\sqrt{72}\)

                                         \(\Leftrightarrow \sqrt{38}< 2\sqrt{14}<3\sqrt{7}< 6\sqrt{2}\)