Q40 of 124 Page 33

Give an example of two irrational numbers whose sum as well as the product is rational.

Let two irrational numbers be 10 + 2√5 and 5 - 2√5
(i) sum is rational
= 10 + 2√5 + 5 - 2√5


= 15 (a rational number)
(ii) product is rational are


= (10 + 2√5) (10 - 2√5)
= (10)2 - (2√5)2
= 100 - 20 = 80 (a rational number)


More from this chapter

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38

Match the following columns:











Column I



Column II



A.


B.


C. The length of period of


D. If then



(p) 14


(q) 6


(r) a rational number


(s) an irrational number



The correct answer is:


(a)-……., (b)-……., (c)-……., (d)-…….,

 39

Match the following columns:











Column I



Column II



A.


B. then x = ……. ,


C. then


D.



(p) 4


(q)


(r)


(s) 3



The correct answer is:


(a)-……., (b)-……., (c)-……., (d)-…….,

 41

If x is rational and y is irrational, then show that (x + y) is always irrational.

 42

Is the product of a rational and an irrational number always irrational?

Give an example.