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?

If a and b are rational, then their squares and their sum, a² + b², are rational. That rational sum does not have to be a perfect square of a rational number; for example, 1² + 1² = 2, and √2 is irrational. Thus c can be irrational, as choice A states.

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