Part a: find a rational number that is between 7.7 and 7.9. explain why it is rational. (2 points)

part b: find an irrational number that is between 7.7 and 7.9. explain why it is irrational. include the decimal approximation of the irrational number to the nearest hundredth. (3 points)

Part A 
7.8 is rational  because it can be written as a fraction 78/100 or 39/50

Part B

7.7^2 = 59.29 and 7.8^2 = 60.84
so an irrational number betwee 7.7 and 7.8 would be  sqrt 60.  Radicals like these ( like sqrt2 , sqrt10 that are not perfect squares)  have irrational square roots).

sqrt 60  = 7.75 to the nearest hundredth

if you try 'square root of 60'on a scientific calculator it usually gives you up to 9 decimal places  Mine gives 7.745966692  but the decimals go on without bounds,

These are the multiples of 15 but what you are probably asking or what are the factors of 15