Answer: √3 and √2 are irrational numbers;
[tex]-\dfracP{1}{16}[/tex] and 0 are rational numbers.
Step-by-step explanation: We are given to classify the following numbers as rational or irrational:
[tex]\sqrt{3},~~-\dfrac{1}{16},~~0,~~\sqrt{2}.[/tex]
Rational number: The digits after the decimal are either repeating or terminating.
Irrational number: The digits after the decimal are non-terminating and non-terminating.
(a) We have
[tex]\sqrt{3}=1.732050807568877~.~.~.[/tex]
Since the digits after the decimal are non-terminating and non-repeating, so √3 is an IRRATIONAL number.
(b) We have
[tex]-\dfrac{1}{16}=-0.0625.[/tex]
Since the digits after the decimal are terminating, so [tex]-\dfrac{1}{16}[/tex] is a RATIONAL number.
(c) We have
[tex]0=0.000.[/tex]
Since the digits after the decimal are terminating, so [tex]0[/tex] is a RATIONAL number.
(d) We have
[tex]\sqrt{2}=1.414213562373095~.~.~.[/tex]
Since the digits after the decimal are non-terminating and non-repeating, so √2 is an IRRATIONAL number.
