Work out rationalise the denominator instantly with clear inputs, formula shown and shareable results.
Multiplying top and bottom by the conjugate b − c√d clears the surd, because (b + c√d)(b − c√d) = b² − c²d is rational. The result splits into a rational part plus a multiple of √d.
Rationalising
a/(b + c√d) = a(b − c√d) / (b² − c²d)
Multiply by (3 − √2)/(3 − √2) to get 6(3 − √2)/7, that is 18/7 − (6/7)√2 ≈ 1.3592455.
It makes fractions easier to compare and to add, and before calculators it made hand computation far simpler.