Is the product of a rational and irrational number always irrational?

Mypequeassenez43

Mypequeassenez43

Answered question

2022-12-07

Is the product of a rational and irrational number always irrational?

Answer & Explanation

Baron Marquez

Baron Marquez

Beginner2022-12-08Added 6 answers

Find the product of rational and irrational numbers.
Both rational and irrational numbers are real numbers, but they have different characteristics. A rational number is a number that can be expressed in the form of the ratioPQ&Q0 and an irrational number cannot be expressed in the ratio PQ&Q0. Although both numbers are different, they are both real and can be represented by a number line.
Example 1: a=23,b=3
Product ab=23
23 is an irrational number.
Example 2: a=0,b=3
Product ab=0
0 is a rational number.
Example 3: a=4,b=3
Product ab=43
43 is an irrational number.
Given the example above, we can infer that if the rational number is 0, the product of the rational number and the non-rational number is always a rational number, but if the rational number is non-zero, the product of the rational number and irrational numbers are always irrational numbers.
Therefore, the given statement is only true when the rational number is no zero.

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