Which numbers are rational numbers and irrational numbers and why

-3.786, 3π, 8/17, 8.23, √11, 10.86731234, 0.75, √.49

See below.

Step-by-step explanation:

A rational number can be written as a fraction a/b where a/b are integers. But irrational numbers cannot be written as a/b.

-3.786 is rational because it can be written as -3 786/1000.

8/17 is of the form a/b so it is rational

 8.23, 10.8673124 and 0.75 are also rational for the same reason as -3.786 is rational.

√0.49 = 0.7 so it is rational.

3π is irrational as π is irrational . π is a non -repeating decimal  which goes on without bounds.

√11 is also irrational - a non repeating decimal like π.