A rope is sqrt(250) units longThe rope is cut into two pieces, so that the lengths of the pieces are in the ratio 3:2 What is the length of the longer piece expressed in simplest radical form?
Let the length of the shorter piece be 3x, where x is a positive constant.
Then the length of the longer piece is 2x.
We know that the sum of the lengths of the two pieces is sqrt(250), so:
3x + 2x = sqrt(250)
5x = sqrt(250)
Squaring both sides of the equation, we have:
25x^2 = 250
Dividing both sides of the equation by 25, we have:
x^2 = 10
Taking the square root of both sides of the equation, we have:
x = sqrt(10)
Therefore, the length of the longer piece is 2x = 2(sqrt(10)).
The length of the longer piece expressed in the simplest radical form is 2(sqrt(10)). Answer: \boxed{2\sqrt{10}}.