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,

Hnmmmn not sure