Question

- Find two irrational number between 0.6 and 0.66.​

Answer 1

solution :

A rational, non-zero number multiplied by an irrational number always results in an irrational number. Knowing this, you can fairly easily choose a rational number to multiply by any given irrational that will be within your stated range.

In this example, I'm going to choose pi (~3.1415926535897932) as the irrational number and x will be the rational number.

So we want to satisfying the following inequality:

0.6 < pi * x < 0.66

Dividing everything by pi (which is positive) gives us:

0.6/pi < x < 0.66/pi

A quick check on the calculator tells us that:

0.6/pi ~= 0.191

0.66/pi ~= 0.21

So, choosing x = 0.20, we end up with 0.2 * pi as our answer. A quick verification with the calculator shows that 0.2 * pi ~= 0.628, so it's between 0.6 and 0.66. Since 0.2 is 1/5, the equivalent pi/5 is a slightly more aesthetic answer.

hope it helps

Jai Hind Jay Bharat