Question

Now consider the product of a nonzero rational number and an irrational number. Again, assume x = , where a and b are integers and b ≠ 0. This time let y be an irrational number. If we assume the product x · y is rational, we can set the product equal to , where m and n are integers and n ≠ 0. The steps for solving this equation for y are shown.
Based on what we established about the classification of y and using the closure of integers, what does the equation tell you about the type of number y must be for the product to be rational? What conclusion can you now make about the result of multiplying a rational and an irrational number?

Answer 1

Answer:

Irrational number

Step-by-step explanation:

It's given,

y = $\frac{mb}{na}$ (By simplifying the product of rational number 'x' and an irrational number 'y')

Where m and n are the integers and $\frac{b}{a}$ is a rational number.

(Since x = $\frac{a}{b}$ is a rational number)

Therefore, $\frac{mb}{na}$ will be a rational number.

y = $\frac{mb}{na}$ ⇒ Irrational number = Rational number

which is a contradictory statement.

Therefore, multiplication of rational and irrational number will be irrational.