Final answer:
The exact length of the hypotenuse of the right triangle is 2√13.
Step-by-step explanation:
The length of the hypotenuse can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, the length of one leg is 4 and the length of the other leg is 6. Plugging these values into the Pythagorean theorem, we have
c^2 = 4^2 + 6^2.
Simplifying this, we get
c^2 = 16 + 36,
which further simplifies to
c^2 = 52.
Taking the square root of both sides, we find that the exact length of the hypotenuse is √52.
To simplify this, we can write it as 2√13.