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Can you multiply two irrational numbers and get an irrational number?
Wiki User
∙ 14y ago
Yes, but not always.
An easy example is sqrt(2)*sqrt(3), which is sqrt(6) and irrational.
An easy counterexample is simply sqrt(2) * sqrt(2), which is 2 and rational.
Wiki User
∙ 14y ago
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Which number produces an irrational number when multiplied by?
At least one of the factors has to be irrational.* An irrational number times ANY number (except zero) is irrational. * The product of two irrational numbers can be either rational or irrational.
Does an irrational number multiplied by an irrational number equal an irrational number?
The product of two irrational numbers may be rational or irrational. For example, sqrt(2) is irrational, and sqrt(2)*sqrt(2) = 2, a rational number. On the other hand, (2^(1/4)) * (2^(1/4)) = 2^(1/2) = sqrt(2), so here two irrational numbers multiply to give an irrational number.
Is the sum of any two irrational number is an irrational number?
The sum of two irrational numbers may be rational, or irrational.
Define irrational numbers?
An irrational number is a number that can't be exactly represented as the ratio of two integers.
Can you add two irrational numbers to get a rational number?
Yes Yes, the sum of two irrational numbers can be rational. A simple example is adding sqrt{2} and -sqrt{2}, both of which are irrational and sum to give the rational number 0. In fact, any rational number can be written as the sum of two irrational numbers in an infinite number of ways. Another example would be the sum of the following irrational quantities [2 + sqrt(2)] and [2 - sqrt(2)]. Both quantities are positive and irrational and yield a rational sum. (Four in this case.) The statement that there are an infinite number of ways of writing any rational number as the sum of two irrational numbers is true. The reason is as follows: If two numbers sum to a rational number then either both numbers are rational or both numbers are irrational. (The proof of this by contradiction is trivial.) Thus, given a rational number, r, then for ANY irrational number, i, the irrational pair (i, r-i) sum to r. So, the statement can actually be strengthened to say that there are an infinite number of ways of writing a rational number as the sum of two irrational numbers.
Is the set of irrational numbers closed under mulriplication?
No. You can well multiply two irrational numbers and get a result that is not an irrational number.
When you multiply two irrational numbers the result is called what?
If you multiply two irrational numbers, the result can be rational, or irrational.
Is the product of two irrational numbers always an irrational number?
No. The square root of two is an irrational number. If you multiply the square root of two by the square root of two, you get two which is a rational number.
Why is it that when you multiply two irrational numbers you get a rational number?
As a general rule you don't; you do if you choose them carefully.
If you add two irrational numbers do you get an irrational number?
Not necessarily. The sum of two irrational numbers can be rational or irrational.
Which number produces an irrational number when multiplied by?
At least one of the factors has to be irrational.* An irrational number times ANY number (except zero) is irrational. * The product of two irrational numbers can be either rational or irrational.
Does an irrational number multiplied by an irrational number equal an irrational number?
The product of two irrational numbers may be rational or irrational. For example, sqrt(2) is irrational, and sqrt(2)*sqrt(2) = 2, a rational number. On the other hand, (2^(1/4)) * (2^(1/4)) = 2^(1/2) = sqrt(2), so here two irrational numbers multiply to give an irrational number.
Will you always get an irrational number when you multiply two irrational numbers if no provide a counterexample?
The square root of 2 times the square root of 2 is rational.
Is the sum of any two irrational number is an irrational number?
The sum of two irrational numbers may be rational, or irrational.
Method to find an irrational number between two irrational numbers?
It is proven that between two irrational numbers there's an irrational number. There's no method, you just know you can find the number.
Are there more rational numbers than irrational numbers true or false?
In between any two rational numbers there is an irrational number. In between any two irrational numbers there is a rational number.
Are more rational numbers than irrational numbers true or false?
In between any two rational numbers there is an irrational number. In between any two Irrational Numbers there is a rational number.
