Question

Which of the following shows that the product of two irrational numbers can be rational?

a.2π/5 x 2/π
b. √2 x √ π
c. 2/π x √2
d. π x √5

Answer 1

The product of two irrational numbers can be rational if and only if their product is rational.

Step-by-step explanation:

In order to show that the product of two irrational numbers can be rational, we need to find an example where the product of two irrational numbers results in a rational number. Let's examine each option:

a. 2π/5 x 2/π = 4/5 ∸ 0.8 (rational)

b. √2 x √ π = √(2π) (irrational)

c. 2/π x √2 = 2√2/π (irrational)

d. π x √5 = π√5 (irrational)

Therefore, the product 2π/5 x 2/π from option (a) shows that the product of two irrational numbers can be rational.