The Mathematics of Multiplying Rational and Irrational Numbers | Why the Result is Always Irrational

product of rational number and irrational number is

When you multiply a rational number by an irrational number, the result is always an irrational number

When you multiply a rational number by an irrational number, the result is always an irrational number.

To understand why, let’s first define what rational and irrational numbers are. A rational number is any number that can be expressed as a fraction, where both the numerator and denominator are integers. For example, 1/2, -3/4, and 7/1 are all rational numbers.

On the other hand, an irrational number is a number that cannot be expressed as a fraction and has an infinite number of non-repeating decimal places. Examples of irrational numbers include π (pi) and √2 (the square root of 2).

Now, let’s consider the product of a rational number, represented by the fraction a/b, and an irrational number, represented by the symbol X. We can express this as (a/b) * X.

To simplify this expression, we need to multiply the numerator a by X and the denominator b by X. Since X is an irrational number, the product of a and X will also be irrational. This is because multiplying an irrational number by any nonzero number (rational or irrational) will not change its irrationality.

Similarly, multiplying the denominator b by X will also result in an irrational number, as the product of a rational number and an irrational number is always irrational.

Therefore, when you multiply a rational number by an irrational number, the product will always be an irrational number.

More Answers:
The Rational or Irrational Results of Adding or Multiplying Irrational Numbers
Understanding Natural Numbers | A Foundation for Mathematical Operations and Concepts
Why Adding a Rational Number and an Irrational Number Always Results in an Irrational Number

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