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 a? + b2 = -2
If a is a rational number and b is a rational number, why could c be an irrational number?

Answer 1

For the value of hypotenuse can be irrational, sum of squares of other two legs might be imperfect square number.

Explanation:

We all know, the Pythagorean theorem can be stated as follows:

The sum of squares of two legs of a right angled triangle is equal to the square of the hypotenuse.

i.e.

`a^2+b^2=c^2`

Where,
`c` is the hypotenuse and
`a, b` are the two other legs of the right angled triangle.

Given that:

`a` and
`b` are rational numbers.

To find:

Situation for which
`c` is irrational.

Square of a rational number is always rational.

So,
`a^(2) , b^(2)` both will be rational.

And sum of squares of two rational numbers will also be rational.

Therefore,
`a^2+b^2` will also be rational.

and

`c = √(a^2+b^2)`

For the value of
`c` can be irrational, sum of squares of other two legs might be imperfect square number.