Question

The product of a rational number and an irrational number is _[blank]_ an irrational number.

Answer 1

Always for 1st qn



sometimes for 2nd qn

Answer 2

Answer:

1.a: Always

2.a:sometimes

Step-by-step explanation:

a.We have to fill correctly word in the blank

Suppose we have a=2 and b=$\sqrt2$

Then , product of a and b=$2\times \sqrt2=2\sqrt2$

Product of rational number and irrational number is always an irrational number .

Therefore, option a is true

a: Always

b.We are given that product of two irrational numbers

Suppose, a=$\sqrt3$

b=4\sqrt3[/tex]

Product of a and b=$\sqrt3\times 4\sqrt3=12$

12 is a rational number .

If a=$\sqrt2,b=\sqrt3$

Product of a and b=$\sqrt2\times \sqrt3=\sqrt6$

Hence, product of  two irrational numbers is sometimes irrational number not always.

Option a is true

A:sometimes