`a, sqrt(8 + 2 sqrt(8) . sqrt(5) + 5) + sqrt(8 - 2 . sqrt 8 . sqrt 5 + 5)`
`= sqrt 8 + sqt 5 + sqrt 8 - sqrt 5`
`= 2 sqrt 8`
`= 4 sqrt 2`
`b, = (sqrt 2 - sqrt 9)(sqrt(9 + 2 sqrt 9 . sqrt 2 + 2))`
`= (sqrt 2 - sqrt 9)(sqrt 9 + sqrt 2)`
`= 2 - 9`
`= -7`
a, Sửa: \(\sqrt{13+4\sqrt{10}}+\sqrt{13-4\sqrt{10}}\)
\(=\sqrt{\left(\sqrt{5}\right)^2+2.\sqrt{5}.2\sqrt{2}+\left(2\sqrt{2}\right)^2}+\sqrt{\left(\sqrt{5}\right)^2-2.\sqrt{5}.2\sqrt{2}+\left(2\sqrt{2}\right)^2}\)
\(=\sqrt{\left(\sqrt{5}+2\sqrt{2}\right)^2}+\sqrt{\left(\sqrt{5}-2\sqrt{2}\right)^2}\)
\(=\left|\sqrt{5}+2\sqrt{2}\right|+\left|\sqrt{5}-2\sqrt{2}\right|\)
\(=\sqrt{5}+2\sqrt{2}-\left(\sqrt{5}-2\sqrt{2}\right)\) (vì \(\sqrt{5}-2\sqrt{2}< 0\))
\(=\sqrt{5}+2\sqrt{2}-\sqrt{5}+2\sqrt{2}=4\sqrt{2}\)
b, \(\left(\sqrt{2}-\sqrt{9}\right)\sqrt{11+2\sqrt{18}}\)
\(=\left(\sqrt{2}-\sqrt{9}\right)\sqrt{\left(\sqrt{2}\right)^2+2\sqrt{2}\sqrt{9}+\left(\sqrt{9}\right)^2}\)
\(=\left(\sqrt{2}-\sqrt{9}\right)\sqrt{\left(\sqrt{2}+\sqrt{9}\right)^2}\)
\(=\left(\sqrt{2}-\sqrt{9}\right)\left|\sqrt{2}+\sqrt{9}\right|\)
\(=\left(\sqrt{2}-\sqrt{9}\right)\left(\sqrt{2}+\sqrt{9}\right)\)
\(=\left(\sqrt{2}\right)^2-\left(\sqrt{9}\right)^2=2-9=-7\)
