The formula for the circumference of a circle is c=pi d, where d is the length of the diameter. If d is a rational number, what can you conclude about the circumference?

Answer :

Answer:

The circumference is an irrational number.

Step-by-step explanation:

[tex] \pi [/tex] is an irrational number, multiplying [tex] \pi [/tex] by a rational number different from 0 will give as a result an irrational number. This is because if that is not the case, then there would exist rational numbers a and b, with a different from 0, such that  [tex] \pi *a = b [/tex], then [tex] \pi = \frac{b}{a} [/tex] .

Since the quotient of two rational numbers is a rational number, if b and a were rational, then [tex] \pi [/tex] should also be rational, which is not the case.

We conclude that, since the diameter is positive and rational, that the circumference cant be rational, therefore it is irrational.

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