(i) Real numbers are numbers which include both rational and irrational numbers. (ii) Every rational number can be expressed as , where p and q are integers and q 0. (iii) Irrational numbers cannot be expressed as , 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 - ) and its rationalising factor a rational number?

Question

KnowledgeBoat · Accepted Answer

(a) No, because rational - irrational = irrational Example : 2 - is an irrational number as 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 - is 3 + = (3 - ) × (3 - ) = (3)2 - = 9 - 7 = 2. 2 is a rational number. Hence, required answer is Yes.

Mathematics

Rational Irrational Nos

Related Questions

Show that x is irrational, if :
(i) x² = 6
(ii) x² = 0.009
(iii) x² = 27

Mathematics

Rational Irrational Nos

Related Questions

Show that x is irrational, if :(i) x2 = 6(ii) x2 = 0.009(iii) x2 = 27

Show that x is irrational, if :
(i) x² = 6
(ii) x² = 0.009
(iii) x² = 27