Step-by-step explanation:
We are given that
[tex]pq = r[/tex]
And that r is a real number. This means that r is a decimal, negative number,interger,fraction, or any number except imaginary numbers.
Let say r=6.
[tex]pq = 6[/tex]
We can use two rational numbers to equal six like 2,3
[tex]2 \times 3 = 6[/tex]
[tex]6 = 6[/tex]
So p and q can be rational numbers.
We can also use two irrational numbers
[tex]pq = 6[/tex]
[tex] \sqrt{18} \times \sqrt{2} = \sqrt{36} [/tex]
[tex] \sqrt{36} = 6[/tex]
so
[tex] \sqrt{18} \times \sqrt{2} = 6[/tex]
Sqr root of 18 and sqr root of 2 are irrational numbers so p and q can be irrational as well.
