The Pythagorean theorem states that the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse by the formula a2 + b2 = c2.If a is a rational number and b is a rational number, why could c be an irrational number?

Squaring rational numbers and adding the results gives a rational number, but that number is not always a perfect square. For example, if a = 1 and b = 1, then c² = 1² + 1² = 2. Since 2 is not a perfect square, c = √2 is irrational; this is why the left side could be a rational non-perfect square.

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