Question

Classify each number as rational or irrational.

Answer 1

Answer:  √3 and √2 are irrational numbers;

                $-\dfracP{1}{16}$ and 0 are rational numbers.

Step-by-step explanation:  We are given to classify the following numbers as rational or irrational:

$\sqrt{3},~~-\dfrac{1}{16},~~0,~~\sqrt{2}.$

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

$\sqrt{3}=1.732050807568877~.~.~.$

Since the digits after the decimal are non-terminating and non-repeating, so √3 is an IRRATIONAL number.

(b) We have

$-\dfrac{1}{16}=-0.0625.$

Since the digits after the decimal are terminating, so $-\dfrac{1}{16}$ is a RATIONAL number.

(c) We have

$0=0.000.$

Since the digits after the decimal are  terminating, so $0$ is a RATIONAL number.

(d) We have

$\sqrt{2}=1.414213562373095~.~.~.$

Since the digits after the decimal are non-terminating and non-repeating, so √2 is an IRRATIONAL number.

Answer 2

√3 → irrational

-1/10 → rational

0 → rational

√2 → irrational