Question

# Q: if{-3/4, sqrt3, 3/sqrt3, sqrt(25/5), 20, 1.11222, 2.5015132,..., 626/262}, find the following 1) Rational numbers? 2) Irrational numbers?

Irrational numbers
$$\displaystyle{Q}:{\quad\text{if}\quad}{\left\lbrace-\frac{{3}}{{4}},\sqrt{{3}},\frac{{3}}{\sqrt{{3}}},\sqrt{{\frac{{25}}{{5}}}},{20},{1.11222},{2.5015132},\ldots,\frac{{626}}{{262}}\right\rbrace}$$,
find the following
1) Rational numbers?
2) Irrational numbers?

2021-01-20
Rational number:
Rational numbers are the numbers that can be expressed in the form of a ratio $$\displaystyle{\left(\frac{{P}}{{Q}}{\quad\text{and}\quad}{Q}\ne{0}\right)}$$
and also if decimal number represents the number after the decimal is repeating, then it is a rational number.
Irrational numbers:
It is impossible to express irrational numbers as fractions or in a ratio of two integers, irrational numbers have endless non-repeating digits after the decimal point.
$$\displaystyle-\frac{{3}}{{4}}$$ It is a rational number.
$$\displaystyle\sqrt{{9}}={3}$$ It is a rational number.
$$\displaystyle\frac{{3}}{\sqrt{{3}}}=\sqrt{{3}}$$ It can not be simplified more, so, it is a irrational number.
$$\displaystyle\sqrt{{\frac{{25}}{{5}}}}=\sqrt{{5}}$$ It can not be simplified more, so, it is a irrational number.
$$\displaystyle{20}=\frac{{20}}{{1}}$$ it is a rational number.
PSK1.11222 it is a rational number because 2 is repeating here.
PSK5.5015132 it is non-recurring and non-terminating. So, it is a irrational number.
$$\displaystyle\frac{{626}}{{262}}$$ it is a rational number.