Question

Is pi + 1 rational or irrational

Answer 1

Answer: Irrational

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Step-by-step explanation:

Let's assume that pi+1 is rational

If so, then pi+1 = m/n where m and n are integers and n is not zero.

Let's isolate pi

pi+1 = m/n

pi = (m/n) - 1

pi = (m/n) - (n/n)

pi = (m - n)/n

This says that pi is rational, as it's in the form integer/integer. But in reality, pi is irrational. The decimal form of pi goes on forever without any known pattern.

So going back to the assumption where we said "pi+1 is rational", that assumption can't be true. If it were true, then it leads to a contradiction. Therefore, pi+1 is irrational.

Answer 2

`\huge\text{Hey there!}`

`\boxed{\huge\text{\boxed{\mathsf{\pi + 1}}}}\\\boxed{\boxed{\huge\text{\boxed{= \mathsf{3.141593 + 1}}}}}\\\\\boxed{\boxed{\huge\text{\boxed{= \bf 4.141593}}}}\\\\\boxed{\huge\text{\boxed{\pi \approx \bold{3.14}\ \& \ 3.14 + 1\ is \approx \bf \underline{\underline{4.14}}}}}`

`\huge\bullet\huge\text{ Pi \boxed{\pi} is an irrational number so any}\\\huge\text{real numbers (0 \& up) cannot be}\\\huge\text{indicated (expressed) by the clearer}\\\huge\text{(simple) fraction\bf (s)}`

`\boxed{\boxed{\huge\text{To \underline{ANSWER} Your question it is: \bf \underline{\underline{irrational}}}}}\huge\checkmark`
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`\boxed{\huge\text{\boxed{\frak {Amphitrite1040:)}}}}`