# Is the product of two irrational number always an irrational number?

## Is the product of two irrational number always an irrational number?

The product of two irrational numbers will not be irrational.

### Can multiplying 2 irrational numbers be rational?

In this case if we multiply √5×√3 we get the answer as √15 or 3.87298335 which is an irrational number. So, from the above two examples we can say that the product of two irrational numbers can be rational sometimes and irrational sometimes.

Is product of a rational number and an irrational number a rational number?

Answer: The product of rational and irrational number is an irrational number. Thus, if rational number is non-zero, the product of a rational and irrational number is always irrational number.

Is 3.141414 a rational number?

D) 3.141141114 is an irrational number because it has not teminating non repeating condition.

## Are all square roots irrational?

Among irrational numbers are the ratio π of a circle’s circumference to its diameter, Euler’s number e, the golden ratio φ, and the square root of two. In fact, all square roots of natural numbers, other than of perfect squares, are irrational.

### Does an irrational number multiplied by an irrational number equal an irrational number examples?

The product of an irrational number and an irrational number is irrational. Only sometimes true (for instance, the product of multiplicative inverses like \sqrt{2} and \frac{1}{\sqrt{2}} will be 1).

What is the difference of irrational and rational numbers?

Rational Number includes numbers, which are finite or are recurring in nature. These consist of numbers, which are non-terminating and non-repeating in nature. Irrational Numbers includes surds such as √2, √3, √5, √7 and so on. Irrational numbers cannot be written in fractional form.

Is a rational times an irrational rational?

If you multiply any irrational number by the rational number zero, the result will be zero, which is rational. Any other situation, however, of a rational times an irrational will be irrational. A better statement would be: “The product of a non-zero rational number and an irrational number is irrational.”