Operations With Irrational Numbers

rational

irrational

rational

irrational

rational number

Irrational Number

Rational Number

Irrational Number

Rational; The sum of two rationals is always rational.

Irrational; The sum of a rational and an irrational is always irrational.

Rational; The product of two rationals is always rational.

Irrational; The product of a nonzero rational and an irrational is always irrational.

Rational; The sum of two rationals is always rational.

Irrational; The sum of a rational and an irrational is always irrational.

Rational; The product of two rationals is always rational.

Irrational; The product of a nonzero rational and an irrational is always irrational.

Rational; The sum of two rationals is always rational.

Sometimes rational, sometimes irrational; The sum of two irrationals is sometimes rational, sometimes irrational.

Rational; The product of two rationals is always rational.

Sometimes rational, sometimes irrational; The product of two irrationals is sometimes rational, sometimes irrational

Rational; The sum of two rationals is always rational.

Irrational; The sum of a rational and an irrational is always irrational.

Rational; The product of two rationals is always rational.

Irrational; The product of a nonzero rational and an irrational is always irrational.

Rational; The sum of two rationals is always rational.

Irrational; The sum of a rational and an irrational is always irrational.

Rational; The product of two rationals is always rational.

Irrational; The product of a nonzero rational and an irrational is always irrational.

Always true

Sometimes true

Never true