Bài 3
\(a,\sqrt{\left(\sqrt{15}-4\right)^2}=\left|\sqrt{15}-4\right|=-\sqrt{15}+4\\ b,=\sqrt{6-2.\sqrt{6}.1+1}\\ =\sqrt{\left(\sqrt{6}-1\right)^2}\\ =\left|\sqrt{6}-1\right|\\ =\sqrt{6}-1\)
Bài 4
\(a,=\left|2\sqrt{3}-3\sqrt{2}\right|+\sqrt{12-2.2\sqrt{3}.1+1}-\sqrt{18+2.3\sqrt{2}.2+4}\\ =3\sqrt{2}-2\sqrt{3}+\sqrt{\left(2\sqrt{3}-1\right)^2}-\sqrt{\left(3\sqrt{2}+2\right)^2}\\ =3\sqrt{2}-2\sqrt{3}+\left|2\sqrt{3}-1\right|-\left|3\sqrt{2}+2\right|\\ =3\sqrt{2}-2\sqrt{3}+2\sqrt{3}-1-3\sqrt{2}-2\\ =-3\)
\(b,=\sqrt{17-6\sqrt{2+\sqrt{8+2.2\sqrt{2}.1+1}}}\\ =\sqrt{17-6\sqrt{2+\sqrt{\left(2\sqrt{2}+1\right)^2}}}\\ =\sqrt{17-6\sqrt{2+\left|2\sqrt{2}+1\right|}}\\ =\sqrt{17-6\sqrt{2+2\sqrt{2}+1}}\\ =\sqrt{17-6\sqrt{\left(\sqrt{2}+1\right)^2}}\\ =\sqrt{17-6\left|\sqrt{2}+1\right|}\\ =\sqrt{17-6\sqrt{2}-6}\\ =\sqrt{11-6\sqrt{2}}\\ =\sqrt{9-2.3.\sqrt{2}+2}\\ =\sqrt{\left(3-\sqrt{2}\right)^2}\\ =\left|3-\sqrt{2}\right|\\ =3-\sqrt{2}\)
`a, sqrt((sqrt 15 - 4)^2)`
`= | sqrt 15 - 4|`
`= 4 - sqrt 15`.
`b, sqrt(7-2 sqrt 6)`
`= sqrt(6 - 2 sqrt 6 + 1)`
`= sqrt((sqrt 6-1)^2)`
`= sqrt 6 - 1`
`a, A = sqrt((2 sqrt 3 - 3 sqrt 2)^2) + sqrt(13-4sqrt3) - sqrt(22+12sqrt2)`
`= | 2 sqrt 3 - 3 sqrt 2| + sqrt(12-4sqrt3 + 1) - sqrt(18 + 12 sqrt 2 + 4)`
`= 3 sqrt 2 - 2 sqrt 3 + 2 sqrt 3 - 1 - (3 sqrt 2 + 2)`.
`= 3 sqrt 2 - 2 sqrt 3 + 2 sqrt 3 - 3 sqrt 2 - 3`
`= -3`
`b, B = sqrt(17-6sqrt(2+sqrt(9+4sqrt2)))`
`= sqrt(17-6sqrt(2+sqrt((2 sqrt 2+1)^2)))`
`= sqrt(17 - 6sqrt(3 + 2 sqrt 2))`
`= sqrt(17 - 6 sqrt((sqrt 2 + 1)^2))`
`= sqrt(17-6(sqrt2+1))`
`= sqrt(11 - 6 sqrt 2)`
`= sqrt(9 - 6 sqrt 2 + 2)`
`= 3 - sqrt 2`.
Bài `3` : Rút Gọn Biểu Thức
`a)` `\sqrt{(\sqrt{15}-4)^2}`
`=|\sqrt{15}-4|`
`=-\sqrt{15}+4`
`b)` `\sqrt{7-2\sqrt{6}}`
`=\sqrt{1-2\sqrt{6}+6}`
`=\sqrt{(1-\sqrt{6})^2}`
`=|1-\sqrt{6}|`
`=-1+\sqrt{6}`
