Question

Select "Rational" or "Irrational" to classify each number;

A. 0.144 Rational or Irrational?
B. √0.144 Rational or Irrational?
C. √0.0144 Rational or Irrational?

Answer 1

⇒A Number is said to be Rational, if it can be written in the form of
`(p)/(q)`, otherwise it is Irrational.

⇒Decimal expansion of Rational is either Terminating or Non Terminating Repeating.For example ,0.234, 0.222222........,

⇒Decimal expansion of Irrational is always "Non Terminating non repeating".For example ,√2,√3, 0.23023002300023.......,

`A.\rightarrow 0.144-----\text{Rational}\\\\B.\rightarrow √(0.144)\\\\=\sqrt{(144)/(1000)}\\\\=(1.2)/(√(10))-----\text{Irrational}`

⇒∵ ,√10, is Irrational.

`C.\rightarrow √(0.0144)\\\\=\sqrt{(144)/(10000)}\\\\=(12)/(100)\\\\=0.12-----\text{Rational}`