Question

is product of a rational number and an rational number,a rrational number ?is product of two irrational number, rational number or irrational number ?justify by giving examples

Answer 1

No,product of a rational number with rational number is a rational number.
2/3 * 4/5 = 8/15
But 8/15 is a rational number.
Also,
Product of two irrational numbers will be sometimes be irrational or rational.
Root 2 * root 6 = root 12
Here root 12 is irrational
And,
Root 2 * root 8 = root 16 = 4
Thus 4 is a rational number.