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What is product of a nonzero rational number and a irrational number?
It is an irrational number.
What is the product of a nonzero rational number and an irrational number?
The product will be irrational.
Is the product of a nonzero rational and a irrational number irrational?
Yes, always.
Are rational numbers is an irrational numbers?
yes * * * * * No. Rational and irrational numbers are two DISJOINT subsets of the real numbers. That is, no rational number is irrational and no irrational is rational.
Is the quotient of two nonzero numbers never a rational number?
The quotient of two nonzero integers is the definition of a rational number. There are nonzero numbers other than integers (imaginary, rational non-integers) that the quotient of would not be a rational number. If the two nonzero numbers are rational themselves, then the quotient will be rational. (For example, 4 divided by 2 is 2: all of those numbers are rational).
Why the product of nonzero rational number and a rational number is an irrational?
Actually the product of a nonzero rational number and another rational number will always be rational.The product of a nonzero rational number and an IRrational number will always be irrational. (You have to include the "nonzero" caveat because zero times an irrational number is zero, which is rational)
Is the product of a nonzero rational number and an irrational number rational or irrational?
It is always irrational.
Is the quotient of two nonzero numbers always a rational number?
Yes, as long as the two nonzero numbers are themselves rational. (Since a rational number is any number that can be expressed as the quotient of two rational numbers, or any number that can be written as a fraction using only rational numbers.) If one of the nonzero numbers is not rational, the quotient will most likely be irrational.
What is product of a nonzero rational number and irrational number is?
It is irrational.
Nonzero rational number and in irrational number makes what?
An irrational number.
What is product of a nonzero rational number and a irrational number?
It is an irrational number.
The product of nonzero rational number and an irrational number is irrational?
Yes.
Is the product of a nonzero rational number and an irrational number irrational?
Yes, always.
What is the product of a nonzero rational number and an irrational number?
The product will be irrational.
Is the product of a nonzero rational and a irrational number irrational?
Yes, always.
Can you multiply an irrational number by a rational number and the answer is rational?
The product of an irrational number and a rational number, both nonzero, is always irrational
Is a rational number divided by an irrational number always irrational?
No. If we let x be irrational, then 0/x = 0 is a counterexample. However, if we consider nonzero rational numbers, then our conjecture is true. We shall prove this by contradiction. Suppose we have nonzero rational numbers x and y, and an irrational number z, such that x/z = y. Since z is not equal to 0, x = yz. Since y is not equal to 0, x/y = z. Since x/y is a quotient of rational numbers, x/y is rational. Therefore, z is rational, contradicting our assumption that z was irrational. QED.
