Question

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?

Answer 1

Because √(a^2+b^2) can be irrational even if a and b are rational.  For the simplest example, let a and b be equal to 1, then c=√2, which is irrational as it cannot be expressed as a ratio of two integers.