Đáp án:
`P=1/2+\sqrt{5}`
Giải thích các bước giải:
`P=\sqrt{{14+3\sqrt{3}}/2}+\sqrt{{16+2\sqrt{15}}/3}-{11\sqrt{3}}/6`
`=\sqrt{{28+2.3\sqrt{3}}/{2^2}}+\sqrt{{15+2\sqrt{15}.1+1^2}/3}-{11\sqrt{3}}/6`
`=\sqrt{{(3\sqrt{3})^2+2.3\sqrt{3}.1+1^2}/{2^2}}+\sqrt{{(\sqrt{15}+1)^2}/3}-{11\sqrt{3}}/6`
`=\sqrt{{(3\sqrt{3}+1)^2}/{2^2}}+|{\sqrt{15}+1}/\sqrt{3}|-{11\sqrt{3}}/6`
`=|{3\sqrt{3}+1}/2|+{\sqrt{15}+1}/\sqrt{3}-{11\sqrt{3}}/6`
`={3\sqrt{3}+1}/2+{2\sqrt{3}.(\sqrt{15}+1)}/{2\sqrt{3}.\sqrt{3}}-{11\sqrt{3}}/6`
`={3.(3\sqrt{3}+1)}/6+{2\sqrt{3}.\sqrt{3}.\sqrt{5}+2\sqrt{3}}/6-{11\sqrt{3}}/6`
`={9\sqrt{3}+3+2.3\sqrt{5}+2\sqrt{3}-11\sqrt{3}}/6`
`={3+6\sqrt{5}}/6=1/ 2 +\sqrt{5}`
Vậy: `P=1/2+\sqrt{5}`
