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RD Chapter 1 Number Systems Ex 1.4 Solutions

Question - 11 : -
Give an example of each, of two irrational numbers whose:
(i) difference is a rational number.
(ii) difference is an irrational number.
(iii) sum is a rational number.
(iv) sum is an irrational number.
(v) product is a rational number.
(vi) product is an irrational number.
(vii) quotient is a rational number.
(viii) quotient is an irrational number.

Answer - 11 : -

Question - 12 : -
Find two irrational numbers between 0.5 and 0.55.

Answer - 12 : -

Two irrational numbers between 0.5 and 0.55 will be 0.51010010001… and 52020020002…

Question - 13 : -
Find two irrational numbers lying betwee 0.1 and 0.12.

Answer - 13 : -

Two irrational numbers lying between 0.1 and 0.12 will be 0.1010010001… and 0.1020020002…

Question - 14 : -
Prove that  is an irrational number.

Answer - 14 : -


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