Yes
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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
It is a rational number because it can be expressed as a fraction in the form of 26/5
26.00
26, known as Fermat's Sandwich Theorem.
Yes. Here's how to prove it. Try dividing 713 by all the primes below its square root. Take the square root, rounded down: 26 Find the largest prime below that: 23 Try dividing 713 by 23, 19, 17, 13, 11, 7, 5, 3, 2 (all the primes from 23 down). It doesn't divide evenly into any of them so it must be prime.