What number is an irrational number that is greater than 7.5?

Answer 1

There are infinitely many Irrational Numbers greater than 7.5 (in fact there are infinitely many between 7.5 and 7.6, and infinitely many between 7.5 and 7.501, etc).

One such number is: 7.50123456789101112131415161718192021222324... where the next decimal digits are the counting numbers (25, 26, 27, etc) - this does not repeat nor does it terminate (as the counting numbers do not terminate) thus it is an irrational number.

Another possible is √56.5, and yet another could be √57

Answer 2

To obtain such a number, take the square root of a number that's greater the square of 7.5 - a number which must not itself be a perfect square. Or add any irrational number to 7.5 - for example, square root of 2, pi, or e. Or if you want your irrational number to be not only greater than 7.5 but also close to it, add something like (pi divided by 1000), (e divided by a million), (square root of 2 divided by a billion), etc.

Answer 3

Oh, there are an infinite number of those.

-- (pi) times (any number greater than 2.4) is one of those.

-- (e) times (any number greater than 2.76) is another one.

-- The square root of the vast majority of numbers greater than 56.25 all are as well, too.