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=[tex]\sqrt2[/tex]
Then , product of a and b=[tex]2\times \sqrt2=2\sqrt2[/tex]
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=[tex]\sqrt3[/tex]
b=4\sqrt3[/tex]
Product of a and b=[tex]\sqrt3\times 4\sqrt3=12[/tex]
12 is a rational number .
If a=[tex]\sqrt2,b=\sqrt3[/tex]
Product of a and b=[tex]\sqrt2\times \sqrt3=\sqrt6[/tex]
Hence, product of two irrational numbers is sometimes irrational number not always.
Option a is true
A:sometimes
