Can a rational number to the power of a rational number be irrational?

Can a rational number raised to the power of an irrational number end up being rational? Are there any examples? – Quora. Yes. 2 and 3 are rational, log 3 ( base 2) is irrational.

Do irrational exponents exist?

An exponent can be an arbitrary real number hence, no matter whether exponent is an integer, a non-integer rational number, or an irrational number it is possible to interpret and calculate that term.

Can a rational number also be an irrational number?

No. A rational number is a number that can be expressed as the quotient of two integers. An irrational number is a number that cannot be expressed as a quotient of two integers. So if a number is either rational or irrational, it cannot also be the other.

Why the sum of rational number and irrational number must be irrational?

Each time they assume the sum is rational; however, upon rearranging the terms of their equation, they get a contradiction (that an irrational number is equal to a rational number). Since the assumption that the sum of a rational and irrational number is rational leads to a contradiction, the sum must be irrational.

Why is the difference of a rational number and an irrational number always irrational?

Therefore, if a rational added or subtracted to an unknown and the result is rational, the unknown is rational. Therefore, a rational plus or minus an irrational is irrational.

Is negative 9 rational or irrational?

-9 is not an irrational number due to a few things. First, let’s take a look at the definition of a rational and irrational number. The definition of an irrational number is this: A real number that cannot be expressed in the form of a/b, (where b cannot equal 0).

Is negative 7 rational or irrational?

A rational number is any number that can be expressed as the quotient of two integers, that is, it can be expressed as a/b, where both a and b are integers and b does not equal zero; The number -7 satisfies the definition of a rational number since it can be expressed in the required form of a/b, i.e., -7 = -7/1 (For …

How do you raise a number to an irrational power?

by definition. Raising a number to an irrational power is no more complicated, in principle, than multiplying a number by an irrational number or, for that matter, multiplying a number by a non-integer rational number.

Is the difference of a rational and irrational numbers always irrational?

The sum of any rational number and any irrational number will always be an irrational number. This allows us to quickly conclude that ½+√2 is irrational. Created by Sal Khan.

Is the difference between a rational and irrational number always irrational?

The sum or difference of a rational number and an irrational number is irrational.

What happens when you raise an irrational number to a rational power?

If you raise an irrational number to a rational power, it is possible to get something rational. For instance, raise Sqrt [2] to the power 2 and you’ll get 2. But what happens if you raise an irrational number to an irrational power?

How do you prove that a number is irrational?

There exist irrational numbers A and B so that A B is rational. Proof. We know that Sqrt [2] is irrational. So, if A=Sqrt [2] and B=Sqrt [2] satisfy the conclusion of the theorem, then we are done. If they do not, then Sqrt [2] Sqrt [2] is irrational, so let A be this number.

Is SQRT [2] Irrational?

We know that Sqrt [2] is irrational. So, if A=Sqrt [2] and B=Sqrt [2] satisfy the conclusion of the theorem, then we are done. If they do not, then Sqrt [2] Sqrt [2] is irrational, so let A be this number.

Is LN2 rational or irrational?

The irrationality of ln2 follows from the generalized irrationality case of for any algebraic number using Hermite-Lindemann theorem. It states that for any algebraic number , the term is transcendental. In particular, for rational values of , cannot be rational.