`a, \sqrt{(3-\sqrt{2})^2} + \sqrt{2(-5)^2}`
`= 3 - \sqrt{2} + 5\sqrt{2}`
`= 3 + 4\sqrt{2}`
`b, \root[3]{625}/\root[3]{5} - \root[3]{-4} . \root[3]{2}`
`= 5^{2/3} \root[3]{5} - (-2)`
`= 5^{2/3} \root[3]{5} + 2`
`c, 6\sqrt{1/2} - 2/(\sqrt{2}) - 3\sqrt{8}`
`= 3\sqrt{2} - \sqrt{2} - 6\sqrt{2}`
`= -4\sqrt{2}`
`d, (\sqrt{6}-\sqrt{3})/(\sqrt{2} - 1) - 2/(\sqrt{3}-1)`
`= ((\sqrt{6}-\sqrt{3})(\sqrt{3}-1)-2(\sqrt{2}-1))/((\sqrt{2}-1)(\sqrt{3}-1))`
`= (\sqrt{2}+\sqrt{3}-1-\sqrt{6})/((\sqrt{2}-1)(\sqrt{3}-1))`
`= -1`
Bài 2 :
`a, \sqrt{(2x-3)^2} = 5`
`⇔ (2x-3)^2 = 5`
`⇔ 2x - 3 = \pm5`
`⇔ 2x = \pm 5 + 3`
`⇔ x = (\pm\sqrt{5}+3)/2`
Vậy `S = {(\pm\sqrt{5}+3)/2}`
`b, \sqrt{9x+9}+\sqrt{4x+4}-\sqrt{16x+16} = 3`
`⇔ 3\sqrt{x+1} + 2\sqrt{x+1} - 4\sqrt{x+1} = 3`
`⇔ \sqrt{x+1} = 3`
`⇔ x + 1 = 3^2`
`⇔ x + 1 = 9`
`⇔ x = 8`
Vậy `S = {8}`
