###### Asked in School SubjectsNumbers Irrational Numbers

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Numbers

Irrational Numbers

# Who was the first person to show that two is an irrational number?

## Answer

###### Wiki User

###### July 29, 2008 5:21AM

No one has ever shown that 2 is an irrational number because it is rational.

## Related Questions

###### Asked in Math and Arithmetic, Algebra, Calculus, Numbers , Irrational Numbers

### Is the set of irrational numbers closed under subtraction?

No; here's a counterexample to show that the set of irrational
numbers is NOT closed under subtraction:
pi - pi = 0.
pi is an irrational number. If you subtract it from itself, you
get zero, which is a rational number. Closure would require that
the difference(answer) be an irrational number as well, which it
isn't. Therefore the set of irrational numbers is NOT closed under
subtraction.

###### Asked in Math and Arithmetic, Numbers , Irrational Numbers

### How do you express irrational number on a number line?

Simply plot the irrational number at it's approximate location
on the number line and label the irrational number.
For example, if you were to plot pi on the number line, you
would plot it at about 3.14 and label it with "π" (the pi symbol,
if it doesn't show up)
Another example is if you want to plot the square root of 2 on
the number line. You would plot it at around 1.414 and label it
with "√2"

###### Asked in Math and Arithmetic, Numbers , Irrational Numbers

### Show that the sum of rational no with an irrational no is always irrational?

Suppose x is a rational number and y is an irrational
number.
Let x + y = z, and assume that z is a rational number.
The set of rational number is a group.
This implies that since x is rational, -x is rational
[invertibility].
Then, since z and -x are rational, z - x must be rational
[closure].
But z - x = y which implies that y is rational.
That contradicts the fact that y is an irrational number. The
contradiction implies that the assumption [that z is rational] is
incorrect.
Thus, the sum of a rational number x and an irrational number y
cannot be rational.

###### Asked in Math and Arithmetic, Algebra, Calculus

### If you take the square root of an irrational number.Will it be irrational too?

Certainly. Otherwise, there would be a rational number whose
square was an irrational number; that is not possible.
To show this, let p/q be any rational number, where p and q are
integers. Then, the square of p/q is (p^2)/(q^2). Since p^2 and q^2
must both be integers, their quotient is, by definition, a rational
number. Thus, the square of every rational number is itself
rational.

###### Asked in Math and Arithmetic, Numbers , Irrational Numbers

### Is -2.2422422242222422224 rational or irrational?

Answer:
-2.2422422242222422224 is rational.
Rational numbers are numbers that can be expressed as the division
of two integers, the divisor not being zero. -2.2422422242222422224
can be expressed as -22422422242222422224 divided by
10000000000000000000.
Answer:
If the number appears exactly as you wrote it in your question,
then the number is rational as explained in the first answer.
However, I wonder if you might have left off the three dot
"continuation symbol" and a "2". Irrational numbers cannot be
properly expressed in decimal form (the decimal representation goes
on forever without repeating), so sometimes we write the first few
digits and put an ellipsis at the end to show they go on forever.
Examples would be
pi = 3.14159...
e = 2.71828...
If you meant to write -2.24224222422224222224... then the number is
(probably) meant to be irrational.

###### Asked in Irrational Numbers

### Why does irrational numbers don't stop?

Because if they stopped they could be expressed as a ratio.
Suppose the decimal expansion of an irrational stopped after x
digit AFTER the decimal point.
Now consider the number n, which is the original number, left
and right of the decimal, but without the decimal point. This is
the nummerator of your ratio. The denominator is 1 followed by x
zeros. It is easy to show that this ratio repesents the decimal
expansion of the number

###### Asked in Math and Arithmetic, Algebra, Numbers , Irrational Numbers

### Why is the square root of 33 irrational?

Most high school algebra books show a proof (by contradiction)
that the square root of 2 is irrational. The same proof can easily
be adapted to the square root of any positive integer, that is not
a perfect square. You can find the proof (for the square root of 2)
on the Wikipedia article on "irrational number", near the beginning
of the page (under "History").