### 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)

### Classify the following number as rational or irrational 0.444444?

The number 0.444444 is a rational number. It is equivalent to 111111/250000, which, by definition of rational numbers, is rational. The number 0.444... (repeating) is also rational because it can be represented by the fraction 4/9. The number 0.444444 is a rational number because a rational number is a nnumber that can be expressed in the form of a fraction.

### Does there exist an irrational number such that its square root is rational?

No, and I can prove it: -- The product of two rational numbers is always a rational number. -- If the two numbers happen to be the same number, then it's the square root of their product. -- Remember ... the product of two rational numbers is always a rational number. -- So the square of a rational number is always a rational number. -- So the square root of an irrational number can't be…

### Is this a rational number 0.131131113?

If you mean to continue the pattern indefinitely, adding more digits, and one more "1" in every cycle, then it is NOT rational. In the case of a rational number, the EXACT SAME group of digits has to repeat over and over (perhaps after some other, initial, digits), for example:0.45113113113113113... Here, the group of digits "113" repeats over and over, so the number is rational.

### Negative fractions are Rational number?

They are rational, if the numerator and denominator are integers. For example, -2 / 3 would be a rational number. They are rational, if the numerator and denominator are integers. For example, -2 / 3 would be a rational number. They are rational, if the numerator and denominator are integers. For example, -2 / 3 would be a rational number. They are rational, if the numerator and denominator are integers. For example, -2 / 3…

### What numbers will produce a rational number when multiplied?

Any number will be a rational number when multiplied.0 multiplied by any real number is rational and so it will produce a rational number when multiplied. If x is any non-zero number (rational or not), then since it is non-zero, 1/x is defined and x*(1/x) = 1 which is rational. So any non-zero number will produce a rational number when multiplied. Thus any number will produce a rational number when multiplied.