30 points. find a rational number and an irrational number that are between 7.7 and 7.9. include the decimal approximation of the irrational number to the nearest hundredth.

7.8 would be a rational number between 7.7 and 7.9. This us found by just choosing a number between those two. To find an irrational number. I suggest going with a radical or square root approach.
Square both 7.7 a d 7.9 and then choose a number in that range that is not a perfect square. This will be your irrational number.
7.7^2 = 59.29
7.9^2 = 62.41
I will be choosing 60, so my irrational number will be

which is equal to approximately 7.75.