Question

write any two irrational numbers between 3 and 4

Answer 1

Step 1: First of all, we arrange our given rational number in relationship order by using an assumed variable ‘y’ like ‘a’ and ‘b’ are two rational number, then,
a < y < b …..................equation (1),
Step 2: After evaluation of certain relation, now we perform arithmetic operation on given equation (1)-
Like we have a relation a < y < b.
Now we subtract √5 from both sides, then difference between the given two rational numbers is same, means ‘a - √5’ and ‘b - √5’ is same value, so-
a - √5 < y < b - √5 …........equation (2)
Step 3: After above two steps, now we solve equation (2 -
a - √5< y < b - √5,
=> a < y + √5 < b,
Addition between irrational number and any number produces an irrational number. So, here ‘y’ is an irrational number.
Now we will discuss irrational number between 3 and 4:
For getting irrational number between 3 and 4, we use following steps-
Step 1: First of all, we get a relation between 3 and 4 by using assumed variable ‘y’-
3 < y < 4 …..............equation (1),
Here ‘y’ is an assume variable,
Step 2: After evaluation of equation (1), now we subtract √7 from both sides, then it produces-
3 - √7 and 4 - √7, so our equation (1)-
3 - √7 < y < 4 - √7,
=> 3 < y + √7 < 4,
So, there is an irrational number ‘y + √7’ which exists between two rational numbers 3 and 4.

Answer 2

Irrational numbers between 3 and 4 are.

1). 32020020002......

2). 3911911191111....