How long is the hypotenuse of a right triangle with legs 9 and 16?

Given the legs of the right triangle as 9 and 16, we use the Pythagorean theorem:

c^2 = a^2 + b^2

Plug in the given values:

c^2 = 9^2 + 16^2

Calculate the squares:

9^2 = 81

16^2 = 256

Add the two squares:

c^2 = 81 + 256

c^2 = 337

Take the square root of both sides:

c = \sqrt{337}

Thus, the length of the hypotenuse is

\sqrt{337}.