Đáp án+Giải thích các bước giải:
`a) ` $\sqrt{8 + 2\sqrt{15}}$
`=` $\sqrt{8 + 2\sqrt{3.5}}$
`=` $\sqrt{8 + 2\sqrt{3}\sqrt{5}}$
`=` $\sqrt{3 + 2\sqrt{3}\sqrt{5}+5}$
`=` $\sqrt{(\sqrt{3)²} + 2\sqrt{3}\sqrt{5}+(\sqrt{5})²}$
`=` $\sqrt{(\sqrt{3} + \sqrt{5} )²}$
`=` | $\sqrt{3}$ + $\sqrt{5}$ |
`=` $\sqrt{3}$ + $\sqrt{5}$
`b)` $\sqrt{3 + \sqrt{8}}$
`=` $\sqrt{3 + 2\sqrt{2}}$
`=` $\sqrt{2 + 2\sqrt{2}\sqrt{1} + 1}$
`=` $\sqrt{(\sqrt{2}²) + 2\sqrt{2}\sqrt{1} + (\sqrt{1}²)}$
`=` $\sqrt{(\sqrt{2} + \sqrt{1})²}$
`=` |$\sqrt{2}$ + $\sqrt{1}$ |
`=` `1`` +` $\sqrt{2}$
`d)` $\sqrt{14 - 6\sqrt{5}}$
`=` $\sqrt{14 - 2.3\sqrt{5}}$
`=` $\sqrt{9 - 2.3\sqrt{5} + 5}$
`=` $\sqrt{3² - 2.3.\sqrt{5} + (\sqrt{5}²)}$
`=` $\sqrt{(3 - \sqrt{5})²}$
`= |3 -` $\sqrt{5}$ |
`= 3 -` $\sqrt{5}$
`e)` $\sqrt{22 - 8\sqrt{6}}$
`=` $\sqrt{22 - 2.4\sqrt{6}}$
`=` $\sqrt{16 - 2.4.\sqrt{6} + 6}$
`=` $\sqrt{4² - 2.4\sqrt{6} + (\sqrt{6}²)}$
`=` $\sqrt{(4 - \sqrt{6})²}$
`= | 4 -` $\sqrt{6}$ |
`= 4 -` $\sqrt{6}$
