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

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There cannot be a proof since your assertion is not necessarily true. sqrt(2)*sqrt(3) = sqrt(6). All three are irrational numbers.

It cannot. It can only show square roots which represent only a small proportion of irrational numbers.

No. The easiest counter-example to show that the product of two irrational numbers can be a rational number is that the product of √2 and √2 is 2. Likewise, the cube root of 2 is also an irrational number, but the product of 3√2, 3√2 and 3√2 is 2.

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.

.1111 is rational. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.

Ellen Degeneres was the first person to be on the show.

zero technically isn't a number. it represents the absence of a number. It's nothing, and it's just used to show when there isn't any number

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"

It is very had to show that but you could approximate it with 22/7. (or just round it to 3.14159265) 22/7=3.142857142857... pi=3.14159265...

Yes. Contributor trust is the number of recommendations that a contributor has received.

It is an irrational number and rounds to 5.66 to the nearest hundredths

"Every rational number" is a single value and there cannot be anything between only one thing!

Root signs didn't show up

There is no simple method. If you can write the number as a ratio of two integers, in the form p/q where q>0, then the number is rational. But it is often very difficult to show that such a representation is not possible.

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.

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.

Cher was the first person to have their belly button shown on tv.

There is no information available to know who was literally the first person to watch the show.

iCarly is a show, not a person, so there is no mobile phone number.

yes because you can always put a whole number over something (the definition of an irrational number being that it can not go over something) for example you can say 1/1 which proves that 1 is a rational number.

The Simpsons first aired on the Tracy Ulman show.

Elvis Presley

The first one I can remember is "Soap" played by Billy Crystal.

Telemachus.

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 bepi = 3.14159...e = 2.71828...If you meant to write -2.24224222422224222224... then the number is (probably) meant to be irrational.