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?

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.

Answer 1

Answer:

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

Explanation:

According to the Pythagorean theorem, the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse.

Take $a=2,b=5$

$a^2+b^2=2^2+5^2=4+25=29$

As $a^2+b^2=c^2$, $c^2=29$

Here, 29 is not a perfect square.

So, c is irrational.

If a is a rational number and b is a rational number, c could be an irrational number as the left side of the equation will result in a rational number, which could be a non-perfect square.

Answer 2

The reason for which the value of c would be an irrational number:-

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

• Pythagoras theorem states that the sum of the square of the base and the perpendicular in a right triangle would be equivalent to the square of the hypotenuse of that triangle.

In the given situation,

$a^2 + b^2 = c^2$

Since a and b are rational numbers, the reason for c being an irrational number would be:

Let's assume $a = 3, b = 5$

Now,

$a^2 + b^2 = c^2$

$3^2 + 5^2 = c^2$

∵ $c = \sqrt{34}$

Hence, c is a non-perfect square as the equations' left side produces a rational number.

Thus, option D is the correct answer.

Learn more about "Pythagoras" here:

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