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Is the sum of two irrational number is always irrational?
No. For example, -root(2) + root(2) is zero, which is rational.Note that MOST calculations involving irrational numbers give you an irrational number, but there are a few exceptions.
Why is the product of a non - zero rational number and an irrational number is irrational?
Let q be a non-zero rational and x be an irrational number.Suppose q*x = p where p is rational. Then x = p/q. Then, since the set of rational numbers is closed under division (by non-zero numbers), p/q is rational. But that means that x is rational, which contradicts x being irrational. Therefore the supposition that q*x is rational must be false ie the product of a non-zero rational and an irrational cannot be rational.
Irrational number when multiplied by 0.4?
If you multiply an irrational number by ANY non-zero rational number, the result will be irrational.
Is 10x 3.14 irrational?
The product of two rational numbers, as in this example, is always RATIONAL.However, if you mean 10 x pi, pi is irrational; the product of a rational and an irrational number is ALWAYS IRRATIONAL, except for the special case in which the rational number is zero.
Is the product of a rational number and an irrational number rational or irrational?
Such a product is always irrational - unless the rational number happens to be zero.
What happens when a rational number is divided by an irrational number?
When a rational numbers is divided by an irrational number, the answer is irrational for every non-zero rational number.
Is zero an irational number?
Zero is a rational number, and therefore is NOT an irrational number. The definition of a rational number is any number that can be expressed as a fraction where the numerator and demoninator are both integers, and the denominator is non-zero. Irrational numbers are all real numbers that are not rational numbers. Since zero qualifies under the definition of a rational number, (0/3, for example), it therefore cannot be an irrational number.
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 multiplying rational and irrational numbers lead to an irrational number result?
Yes, but only if the rational number is non-zero.
Are there any irrational numbers?
Yes. In fact, almost all real numbers are irrational numbers. An irrational number is any number that cannot be expressed as a ratio of two non-zero integers. Examples of irrational numbers are pi (3.14159.....) and e (2.718.....).
Does an irrational number times an irrational number equal an irrational number?
Not always. For example sqrt(2) and 1/sqrt(2) are both irrational, but their product is the rational number 1.
Rational and irrational numbers are complex numbers?
Rational and irrational numbers are real numbers. A complex number is represented by a+bi where a and b are real numbers. Zero is a real number therefore any real number is also complex whenever b=0
Is negative 2pi a rational number?
No. The number pi is irrational, and if you multiply an irrational number by a non-zero rational number (in this case, -2), you will get another irrational number.As a general guideline, most calculations that involve irrational numbers will again give you an irrational number.
0 is not in the set of?
You can invent an infinite number of sets that don't contain the number zero. For a start, a common set that doesn't contain the zero is the set of natural, or counting, numbers (1, 2, 3...).You can invent an infinite number of sets that don't contain the number zero. For a start, a common set that doesn't contain the zero is the set of natural, or counting, numbers (1, 2, 3...).You can invent an infinite number of sets that don't contain the number zero. For a start, a common set that doesn't contain the zero is the set of natural, or counting, numbers (1, 2, 3...).You can invent an infinite number of sets that don't contain the number zero. For a start, a common set that doesn't contain the zero is the set of natural, or counting, numbers (1, 2, 3...).
Is the sum of two irrational number is always irrational?
No. For example, -root(2) + root(2) is zero, which is rational.Note that MOST calculations involving irrational numbers give you an irrational number, but there are a few exceptions.
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 can irrational numbers be defined as?
In mathematics, an irrational number is any real number which cannot be expressed as a fraction a/b, where a and b are integers, with b non-zero, and is therefore not a rational number
