Question

write five irrational number between 1 and 2​

Answer 1

Answer:

Infinite, so look irrational number between 1 and 2 means that it is going to have a value greater than 1 and less than 2 I believe you can think of many numbers they all will be in decimal following the condition You provided 1<x<2; just to provide more clarifications look at the following example I am providing :→

√2=1.414(approx)

1.2426374

1.2355………..

so on and so forth .

Step-by-step explanation:

Answer 2

Both 1 and 2 are rational number (because they can be expressed in terms of ratios ex: 1=5/5 and 2=24/12 e.t.c)

Now our job is to see how many irrational number there are between two rational number (here it is 1 and 2)

Let's say a=1 and b=2 then our numbers should be between a and b i.e. if the number is x

a<x<b.

Now let's see what's an irrational number. Do you Know what does irrational mean? Something that doesn't make sense right? Off course.

If you explore the digits of √2 you see that decimal expansion is non ending non repeating, and something that doesn't end and doesn't repeat, does that make any sense? How could you possibly write it in terms of ratios?

And we know that that value of √2 goes like this 1.41421356… .. and that's between 1 and 2. Therefore √2 is one such irrational number.

Now if I write number like this 1.010010001 … that doesn't repeat nor end ( what should we call this number?) irrational right? (Yes).

But as you can see you can find many such pattern, for eg. 1.2001000100001 …, 1.2020020002 …. e.t.c