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One way to simplify this expression is to

• turn it into an algebraic number
• then transform that algebraic number back into a symbolic expression.

Here is how to do that.

sage: a = 2*(2378*sqrt(2) - 3363)/(408*sqrt(2) - 577)
sage: AA(a).radical_expression()
-4*sqrt(2) + 6

One way to simplify this expression is toin two steps:

• turn it into an algebraic number
• then transform that algebraic number back into a symbolic expression.expression

Here is how to do that.

sage: a = 2*(2378*sqrt(2) - 3363)/(408*sqrt(2) - 577)

Turn it into an algebraic number:

sage: b = AA(a)
sage: b
0.343145750507?

Turn that algebraic number into a symbolic expression:

sage: c = b.radical_expression()
sage: c
-4*sqrt(2) + 6

Or all in one go:

sage: AA(a).radical_expression()
-4*sqrt(2) + 6