ToNumberField[{Sqrt[6], Sqrt[15],Sqrt[10]}]

Input

Result

${AlgebraicNumber[root of x^4 - 62 x^2 - 240 x - 239 near x = 9.48475, {25/12, 43/12, 5/12, -1/12}], AlgebraicNumber[root of x^4 - 62 x^2 - 240 x - 239 near x = 9.48475, {59/3, 61/6, 1/3, -1/6}], AlgebraicNumber[root of x^4 - 62 x^2 - 240 x - 239 near x = 9.48475, {-87/4, -51/4, -3/4, 1/4}]}$