Đáp án: + Giải thích các bước giải:
`a) \sqrt{(1-\sqrt{5})^2} + 1`
`= \sqrt{5} - 1 + 1`
`= \sqrt{5}`
`b) \sqrt{3+2\sqrt{2}} - \sqrt{3-2\sqrt{2}}`
`= \sqrt{2} + 1 - (\sqrt{2}-1)`
`= \sqrt{2}+1-\sqrt{2}+1`
`= 2`
`c) (2+\sqrt{3})\sqrt{7-4\sqtr{3}}`
`= (2+\sqrt{3})(2-\sqrt{3})`
`= 2^2 - (\sqrt{3})^2`
`= 4 - 3`
`= 1`
`d) 2\sqrt{3+\sqrt{5-\sqrt{13+2\sqrt{12}}}}`
`= 2\sqrt{3+\sqrt{5-\sqrt{(\sqrt{4})^2(\sqrt{3})^2+4\sqrt{3}+(\sqrt{1})^2}}}`
`= 2\sqrt{3+\sqrt{5-\sqrt{(2\sqrt{3}+1)^2}}}`
`= 2\sqrt{3+\sqrt{5-(2\sqrt{3}+)}}`
`= 2\sqrt{3+\sqrt{(\sqrt{1})^2(\sqrt{3})^2-2\sqrt{3}+(\sqrt{1})^2}}`
`= 2\sqrt{3+\sqrt{3}-1}`
`= 2\sqrt{2+\sqrt{3}}`
`e) \sqrt{21+12\sqrt{3}}`
`= \sqrt{(\sqrt{3})^2(\sqrt{3})^2+12\sqrt{3}+(\sqrt{12})^2}`
`= \sqrt{(\sqrt[3}\sqrt{3}+2\sqrt{3})^2}`
`= \sqrt{3}\sqrt{3}+2\sqrt{3}`
`= 3 + 2\sqrt{3}`
`f) 4\sqrt{(-3)^6}+5\sqrt{(-2)^4}-\sqrt{(\sqrt{8}-7)^2} - \sqrt{8}`
`= 3^3*4+2^2*5-(7-2\sqrt{2})-2\sqrt{2}`
`= 108+20-(7-2\sqrt{2})-2\sqrt{2}`
`= 108+20-7+2\sqrt{2}-2\sqrt{2}`
`= 121`