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?

the square of rational numbers is irrational, and sum of two irrational numbers is irrational.

the product of two rational numbers is rational, and the sum of two rational numbers is irrational.

the left side of the equation will result in a rational number, which is a perfect square.

the left side of the equation will result in a rational number, which could be a non-perfect square.

Last option is correct i.e

The left side of the equation will result in a rational number, which could be a non-perfect square.

Step-by-step explanation:

Given that 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

we have to tell if a is a rational number and b is a rational number, why could c be an irrational number.

As, a and b both are rational then their squares are also rational and the addition of two rational numbers are also rational.

Therefore, the only option which gives the c irrational is the square root of .

Hence, last option is correct i.e

The left side of the equation will result in a rational number, which could be a non-perfect square.

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step-by-step explanation:

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