Question

he product of a non-zero rational number and an irrational number can always be written as

a)a fraction.
b)a terminating decimal.
c)a non-repeating, non-terminating decimal.
d)a repeating decimal

Answer 1

The product of a rational and irrational number is an irrational number.

c) a non-repeating, non-terminating decimal

Answer 2

Answer with explanation:

⇒Consider a Non Zero Rational Number = 2, 3, $\frac{2}{3}$, 53,....

The decimal Expansion of Rational number is Either terminating or  Non Teminating repeating.

⇒ Irrational Number = π, √2,√7,...

The decimal Expansion of Irrational number is Non terminating Non repeating.

⇒Product of a non-zero rational number and an irrational number

  =2 ×√2 or 3 × √2 or 3 π

are all Irrational number.

In terms of decimals:

                     (c)⇒a non-repeating, non-terminating decimal=(Irrational Number)

Option C