what is the possible range of answers for:

Find an irrational number between 7 and 8.

The circumference of a circle is 4cm. Find the radius giving your answer as an irrational number.

The area of a circle is 9cm^2. Find the radius, giving your answer to an irrational number.

Find a rational number between square root of 11 and sqrt13.

Find an irrational number between 2 and 3.

Find two different irrational numbers whose product is rational.
 1. An irrational number between 7 and 8 could be 7.1 followed by an infinite, non-repeating sequence of numbers. For example, 7.1 followed by the digits of pi (3, 1, 4, 1, 5, 9, ...) would work. There are infinitely many irrational numbers in this interval, so there is no single "possible range" of answers.

2. The formula for the circumference of a circle is C = 2πr, so if the circumference is 4 cm, then the radius r is given by r = C / (2π). Substituting C = 4 cm, we get r = 4 cm / (2π) = 2 cm / π. This is an irrational number, since π is irrational.

3. The formula for the area of a circle is A = πr^2, so if the area is 9 cm^2, then the radius r is given by r = sqrt(A / π). Substituting A = 9 cm^2, we get r = sqrt(9 cm^2 / π) = 3 cm / sqrt(π). This is an irrational number, since π is irrational.

4. To find a rational number between sqrt(11)
Possible answers for the first question: 7.4, 7.6, 7.8, 8.0. Possible answers for the second question: 2.2, 2.4, 2.6, 2.8. Possible answers for the third question: 3.4, 3.6, 3.8, 4.0. Possible answers for the fourth question: 1.2, 1.4, 1.6, 1.8. Possible answers for the fifth question: 5, 5.2, 5.4, 5.6.