### Instruction: Minneapolis-St. Paul International Airport is 8 miles southwest of downtown St. Paul and 10 miles southeast of downtown Minneapolis. To the nearest integer, how many miles apart are   downtown St. Paul and downtown Minneapolis?### Response: I need to find the distance between two cities that form a right triangle with the airport.
I can use the Pythagorean theorem to find the length of the hypotenuse, which is the distance I want.
The Pythagorean theorem says that a^2 + b^2 = c^2, where a and b are the legs of the right triangle and c is the hypotenuse.
I can label the sides of the triangle as follows: a = 8, b = 10, and c = d, where d is the distance between the cities.
Plugging these values into the Pythagorean theorem, I get 8^2 + 10^2 = d^2.
Simplifying, I get 64 + 100 = d^2, or 164 = d^2.
Taking the square root of both sides, I get d = sqrt(164).
I need to round this to the nearest integer, so I can use a calculator or an approximation.
I know that sqrt(164) is slightly more than 12, because 12^2 = 144 and 13^2 = 169.
So the nearest integer to sqrt(164) is 13.
Therefore, the distance between downtown St. Paul and downtown Minneapolis is 13 miles.