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`A=sqrt{6-4sqrt{2}}+sqrt{19-6sqrt{2}}`

`=sqrt{4-4sqrt{2}+2}+sqrt{18-6sqrt{2}+1}`

`=sqrt{2^2-2.2.sqrt{2}+(sqrt{2})^2}+sqrt{(3sqrt{2})^2-2.3sqrt{2}.1+1^2}`

`=sqrt{(2-sqrt{2})^2}+sqrt{(3sqrt{2}-1)^2}`

`=|2-sqrt{2}|+|3sqrt{2}-1|`

`=2-sqrt{2}+3sqrt{2}-1`

`=2sqrt{2}+1`

Vậy `A=2sqrt{2}+1.`