Question

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

Which word correctly fills in the blank to create a true statement?

always


sometimes


never

The product of two irrational numbers is _[blank]_ an irrational number.
Which word correctly fills in the blank to create a true statement?

sometimes


always


never

Answer 1

always for 1st qn



sometimes for 2nd qn

Answer 2

1.a: Always

2.a:sometimes

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* \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* 4\sqrt3=12`

12 is a rational number .

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

Product of a and b=
`\sqrt2* \sqrt3=\sqrt6`

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

Option a is true

A:sometimes