Question

If p and q are non-zero rational numbers, and s and t are irrational numbers, which statement is possibly true?

a)the product of pq is irrational
b)the product of pt is rational
c)The quotient p over q is irrational.
d)The quotient s over t is rational.

Answer 1

Explanation:

only d can be correct,but not always.

let s=√8 (irrational)

t=√2 (irrational)

s/t=√8/√2=√(4×2)/√2=2√2/√2=2 (rational)

so d is true.

again take another example

let s=π (irrational)

t=√2

s/t=π/√2 (irrational)

d is not true.