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Irrational Numbers are not closed under any of the fundamental operations. You can always find cases where you add two irrational numbers (for example), and get a rational result. On the other hand, the set of real numbers (which includes both rational and irrational numbers) is closed under addition, subtraction, and multiplication - and if you exclude the zero, under division.

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โˆ™ 2013-11-27 12:05:18
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A polynomial of degree zero is a constant term

The grouping method of factoring can still be used when only some of the terms share a common factor A True B False

The sum or difference of p and q is the of the x-term in the trinomial

A number a power of a variable or a product of the two is a monomial while a polynomial is the of monomials

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Q: What are irrational numbers closed under?
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Related questions

Is the set of irrational numbers closed under addition?

no it is not


What operations are irrational numbers closed under?

None.


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.


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.


What answer choice shows that the set of irrational numbers is not closed under addition?

Hennd


Are a set of irrational numbers closed under exponents?

No. Sqrt (2) is irrational. Square it, or raise it to any even power, and it becomes rational. The set is not closed under exponentiation.


Are irrational numbers closed under subtraction?

No, they are not. An irrational number subtracted from itself will give 0, which is rational.


Are irrational numbers closed under division?

No. 4 root 2 and 2 root 2 are both irrational. Divide the first by the second you get 2. Which is not a member of the set of irrational numbers.


Can you add two rational numbers and get an irrational number?

No. The set of rational numbers is closed under addition (and multiplication).


Are irrational numbers closed under addition?

No. For example, the sum of pi and -pi is zero, which is rational - while each of the addends is irrational.


Are irrational numbers closed under multiplication?

No. To say a set is closed under multiplication means that if you multiply any two numbers in the set, the result is always a member of the set. If, say, the 2 numbers are radical 2 and radical 2 we have (1.4142...)(1.4142...) which by definition equals 2. The result is not an irrational number, so the set is not closed.


Is the set of irrational numbers closed under division?

No, it is not. Root2 and root 8 are each irrational. Root8 / root2 =2. 2 is not a member of the set.

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