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State whether 2.5 + π is rational or irrational. Explain.

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Facundo3141592idn

Answer: 2.5 + π is an irrational number.

Step-by-step explanation:

Irrational numbers are numbers that can not be written as the quotient of two integer numbers, and they have an infinite number of digits after the decimal point (such that there is not periodicity in these digits).

So suppose that we have an irrational number and we add 1, then the infinite digits after the decimal point will still be there, so the sum will be also an irrational number.

The same can be seen for the sum between an irrational number and a rational number, where the infinite number of decimals after the decimal point will still be there (because the rational numbers have a finite or infinite but periodical decimals after the decimal point), so the sum between an irrational number and a rational number is always irrational.

In this case, we have the addition:

2.5 + π

Which is the sum of a rational number and an irrational number, so we can conclude that this is an irrational number.

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