Please answer them in detail Show steps please Thank you Wri

Please answer them in detail. Show steps please. Thank you!

Write 0.12bar as p/q where p, q elements of Q and show your work. Produce an irrational number between 4 and 5. Justify your answer.

Solution

1.

Let, x=0.121212...

100x=12.121212...

100x-x=12

99x=12

x=4/33

2.

sqrt{2}=1.41...

and it is an irrational number

3+sqrt{2} is also irrational as sum of rational and irrational is irrational

3+sqrt{2}=4.41.....

So, 3+sqrt{2} is required irrational number