(i) Real numbers are numbers which include both rational and irrational numbers.

(ii) Every rational number can be expressed as $\dfrac{p}{q}$, where p and q are integers and q ≠ 0.

(iii) Irrational numbers cannot be expressed as $\dfrac{p}{q}$, where p and q are integers and q ≠ 0.

Answer the following questions :

(a) Is the difference between a rational number and an irrational number always rational?

(b) Is 0.5555 ……. a rational number ?

(c) Is 0.505005 …… a rational number ?

(d) Is the product of irrational number (3 - $\sqrt{7}$) and its rationalising factor a rational number?

(a) No, because rational - irrational = irrational

Example : 2 - $\sqrt{3}$ is an irrational number as $\sqrt{3}$ is an irrational number.

Hence, required answer is no.

(b) As 0.5555 is a repeating decimal number, so it is a rational number.

Hence, required answer is Yes.

(c) 0.505005 is non-terminating and non-repeating number.

So it is an irrational number, not a rational number.

Hence, required answer is No.

(d) Rationalizing factor of 3 - $\sqrt{7}$ is 3 + $\sqrt{7}$

= (3 - $\sqrt{7}$) × (3 - $\sqrt{7}$)

= (3)² - $(\sqrt{7})^2$

= 9 - 7

= 2.

2 is a rational number.

Hence, required answer is Yes.