State which of following real numbers are :

-8, 0, ${\sqrt5}$, $\dfrac{5}{7}$, $-{\sqrt{18}}$, ${\sqrt{32}}$, 4.28, π, 3, $-\dfrac{8}{15}$, 0.075

(i) rational

(ii) irrational

(iii) positive integers

(iv) negative integers

(v) neither positive nor negative.

(i) rational : -8, 0, $\dfrac{5}{7}$, 4.28, 3, $-\dfrac{8}{15}$, 0.075

Reason : All numbers that can be expressed in the form $\dfrac{p}{q}$, q ≠ 0 and p, q are integers are called rational numbers.

(ii) irrational : ${\sqrt5}$, $-{\sqrt{18}}$, ${\sqrt{32}}$, π

Reason : Numbers that cannot be expressed in the form $\dfrac{p}{q}$ are called irrational numbers.

(iii) positive integers : 3

Reason :Positive integers are whole numbers greater than 0, excluding fractions and decimals.

(iv) negative integers : -8

Reason :Negative integers are whole numbers less than 0, excluding fractions and decimals.

(v) neither positive nor negative : 0

Reason :The number 0 is neutral and does not fall under positive or negative categories.