Today we'll explore one of the most famous mathematical relationships: the Pythagorean theorem. We'll verify that 3 squared plus 4 squared equals 5 squared using a right triangle with sides of length 3, 4, and 5.
Let's start by calculating 3 squared. When we square a number, we multiply it by itself. So 3 squared equals 3 times 3, which equals 9. We can visualize this as a square with side length 3, containing 9 unit squares.
Now let's calculate 4 squared. Four squared equals 4 times 4, which equals 16. We can visualize this as a square with side length 4, containing 16 unit squares arranged in a 4 by 4 grid.
Now we add the results together. We have 3 squared equals 9, and 4 squared equals 16. Adding these together: 9 plus 16 equals 25. So 3 squared plus 4 squared equals 25.
Finally, let's verify that 5 squared equals 25. Five squared equals 5 times 5, which equals 25. This confirms our Pythagorean theorem: 3 squared plus 4 squared equals 5 squared, or 9 plus 16 equals 25. The statement is true! This demonstrates the beautiful relationship in right triangles where the sum of squares of the two shorter sides equals the square of the hypotenuse.