If x and y are rational numbers and non-zero, their sum x + y will also be a rational number. Therefore, the value of the expression x + y is rational.
If y is rational and z is irrational, their sum y + z will be irrational. Therefore, the value of the expression y + z is irrational.
When you multiply two non-zero rational numbers, the product will always be rational. Therefore, the value of the expression xy is rational.
When you multiply a rational number by an irrational number, the product will always be irrational. Therefore, the value of the expression xz is irrational.
Let x and y be non-zero, rational numbers and let z be an irrational number. In the first column of the table below is an expression. In the second column, determine whether the value of each expression is rational or irrational.
Expression Value of Expression
x + y
Rational
y + z
Rational
xy
Irrational
xz
Irrational
1 answer