Sums & products of rational/irrational numbers

Determine whether various combinations of rational and irrational numbers are rational or irrational themselves.

Proof: sum & product of two rationals is rational

Proof: product of rational & irrational is irrational

Proof: sum of rational & irrational is irrational

Sums and products of irrational numbers

Worked example: rational vs. irrational expressions

Worked example: rational vs. irrational expressions (unknowns)

Rational vs. irrational expressions