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 A squared plus b squared is equal to c squared If A is a rational number and b is a rational number, why could c be an irrational number?

Squaring rational numbers and adding them gives a rational number, but that result is not always the square of a rational number. For example, if A = 1 and b = 1, then c² = 1² + 1² = 2, so c = √2, which is irrational. Thus the left side can be rational without being a perfect square, as choice A states.

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