Give an example of each, of two irrational numbers whose: (i) difference is a rational number.

(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, (5√2) - (√2) = 4√2

4√2  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, (4√6) + (√6) =  5√6

5√6 is the rational number.

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

 Now, 2√3 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, 3√6 /√6 = 3

3 is the rational number. 

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

 Now,√6/√2 = √3 + 2/√2 

=√3 x √2/ √2

= √3

√3 is an irrational number