Pythagorean Theorem Calculator

Step-by-step solution

1. 1

   The Pythagorean theorem

   In a right triangle, the square of the hypotenuse equals the sum of the squares of the two legs.

   $$a^2 + b^2 = c^2$$
2. 2

   Substitute the known sides

   Substitute the legs a = 3 and b = 4 into the theorem.

   $$3^2 + 4^2 = c^2$$
3. 3

   Compute exactly

   Square each leg and add: 9 + 16 = 25. Fraction arithmetic keeps this exact.

   $$3^2 + 4^2 = 25$$
4. 4

   Take the square root

   Take the square root of both sides: c = √25.

   $$c = \sqrt{25}$$
5. 5

   Simplify the radical

   The value under the root, 25, is a perfect square, so the answer is exactly 5, with no radical left.

   $$c = \sqrt{25} = 5$$
6. 6

   Result

   With legs a = 3 and b = 4, the hypotenuse is c = 5 ≈ 5.

   $$c = 5 \approx 5$$