Question

What is an irrational number between 7.7 and 7.9 explain why it is irrational. And include the decimal approximation of the irrational number to the nearest hundredth . HELP PLEASE!!

Answer 1

1st- An irrational number is a non terminating decimal and a non repeating decimal also: Examples:
a) 10.5494737891157.... is an irrational number (decimal will continue for ever
b) 15.1231231213123123123.....(Not irrational because decimal are repeating for ever
c) 121.1201200120001200001... (Rational because decimal go foe ever and they are not being repeated.
Now we have to find an irrational number between 7.7 and 7.9 (obviously there are an infinity of such numbers: So

7.7<x<7.9.Take any number between 7.7 and 7.9, say 7.8 and add to its decimal whatever number of digits you may choose. But to be on the safe side I would advise the following (non repeated) number:
7.810 100 1000 10000 10000.....

Answer 2

nightowlIt can be proven that between any two real numbers there exists a rational number. Therefore there exists a rational number r such that
7.7+2–√<r<7.9+2–√By calculator we can find a rational number r that satisfies these condition, I choose 9.2. Now subtract square root 2.7.7<9.2−2–√<7.9

so the answer is between 7.7 and 7.9
rational number : 7.8
irrational number : 9.2 - √2