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Coordinates using Pythagorean Theorem. Enter the number that goes beneath the radical symbol.

Ths number that goes beneath the radical symbol is 29.

Explanation:

If we form a triangle using the given points, we drop a vertical line from     (1, 1) and a horizontal line to the left of (3, -4). The point where both the lines intersect is the third point. The other point is (1, -4).The vertical distance from (1, 1) and (1, -4) is 1 - (-4) = 1 + 4 = 5 units,                          the horizontal distance from (1, -4) and (3, -4) is 3 -1 = 2 units.The opposite side of the triangle measures 5 units while the adjacent side measures 3 units. The line joining (1, 1) and (3, -4) is the hypotenuse. Assume the hypotenuse measures x units.According to Pythagoras theorem, x = √(5² + 2²), x = √25 + 4 = √29. So the number under the radical symbol is 29.