Finding the Hypotenuse

To find the hypotenuse from the two legs, square each leg, add the two squares, and take the square root of the sum. The square root is the last step, because the theorem gives c^2, and the length c is its positive square root. With legs 3 and 4:

Legs 3 and 4: how long is c?

c = √(3^2 + 4^2)

c = √(9 + 16)

c = √(25) = 5

The hypotenuse is 5.

Square each leg on its own, then add the squares, and only then take the square root. Do not add the legs first and square the sum. That would give (3 + 4)^2 = 49 and a hypotenuse of 7, which is wrong. The correct calculation is √(3^2 + 4^2) = 5.