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 $\frac{p}{q}$, 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.......,

$A.\rightarrow 0.144-----\text{Rational}\\\\B.\rightarrow \sqrt{0.144}\\\\=\sqrt{\frac{144}{1000}}\\\\=\frac{1.2}{\sqrt{10}}-----\text{Irrational}$

⇒∵ ,√10, is Irrational.

$C.\rightarrow \sqrt{0.0144}\\\\=\sqrt{\frac{144}{10000}}\\\\=\frac{12}{100}\\\\=0.12-----\text{Rational}$