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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?

The Pythagorean theorem states that the sum of the squares of the legs of a right-example-1
User Mattpr
by
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1 Answer

3 votes

Answer:

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.

User Thomas Bachem
by
8.1k points

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