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Johann Heinrich Lambert

Q: Who was the first person to prove that pi was not a rational number?

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It's the ratio of 121 to 1, so it's rational. I think the square of any rational number is a rational number. In fact, I'm sure of it, because I know how I could prove it.

No, they are not. 1/2 is a ratio of two integers and so it is rational. But it is not a whole number.

(A): 6.34*100 = 634 so 6.34 = 634/100 a ratio of two integers and so a rational number. (B): 6.34 is a terminating decimal - with two non-zero digits after the decimal point. So again, it is a rational number.

2 and 1/2 are rational numbers, but 2^(1/2) is the square root of 2. It is well known that the square root of 2 is not rational.

If the number can be expressed in the form a/b where a and b are both integers and b ≠ 0, then it is proved rational. If you want to prove that it is irrational, then there are many complicated and different steps depending on the type of irrational number. (Yes there are different types)

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Johann Heinrich Lambert

Johann Lambert

It must be a generalised rational number. Otherwise, if you select a rational number to multiply, then you will only prove it for that number.

No, and I can prove it: -- The product of two rational numbers is always a rational number. -- If the two numbers happen to be the same number, then it's the square root of their product. -- Remember ... the product of two rational numbers is always a rational number. -- So the square of a rational number is always a rational number. -- So the square root of an irrational number can't be a rational number (because its square would be rational etc.).

It's the ratio of 121 to 1, so it's rational. I think the square of any rational number is a rational number. In fact, I'm sure of it, because I know how I could prove it.

No, they are not. 1/2 is a ratio of two integers and so it is rational. But it is not a whole number.

9.546 as an improper fraction in its simplest form is 4773/500 which proves that it is a rational number

If the number can be expressed as a ratio of two integer (the second not zero) then the number is rational. However, it is not always a simple matter to prove that if you cannot find such a representation, then the number is not rational: it is possible that you have not looked hard enough!

Benjamin Franklin was the first person to prove that lightning is a form of electricity.

(A): 6.34*100 = 634 so 6.34 = 634/100 a ratio of two integers and so a rational number. (B): 6.34 is a terminating decimal - with two non-zero digits after the decimal point. So again, it is a rational number.

You cannot, because the statements are false! (The second is rational only if r = 0).

1.6 = 16/10.This is a ratio in which both the numerator (16) and denominator (10) are integers. The ratio, therefore, represents a rational number.