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
A
The square of rational numbers is irrational, and sum of two irrational numbers is irrational.
B
The product of two rational numbers is rational, and the sum of two rational numbers is irrational.
C
The left side of the equation will result in a rational number, which is a perfect square.
D
The left side of the equation will result in a rational number, which could be a non-perfect square.