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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.

1 Answer

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(i) √3 is an irrational number.

Now, (3) - (3) = 0

0 is the rational number. 

(ii) Let two irrational numbers are 5√2 and√2

Now, (52) - (2) = 42

42  is the rational number.

(iii) Let two irrational numbers are√11 and -√11

Now, (11) + (-11) = 0 

0 is the rational number. 

(iv) Let two irrational numbers are 4√6 and√6

Now, (46) + (6) =  56

56 is the rational number.

(v) Let two irrational numbers are 2√3 and √3

 Now, 23 x 3 = 2 x 3

= 6

6 is the rational number. 

(vi) Let two irrational numbers are √2 and √5

 Now,  2 x 5 = 10

10 is the rational number.

(vii) Let two irrational numbers are 3√6 and √6

 Now, 36 /6 = 3

3 is the rational number. 

(viii) Let two irrational numbers are√ 6 and √2

 Now,6/2 = 3 + 2/

=3 x 2/ 2

3

3 is an irrational number

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