product of rational number and irrational number is
The product of a rational number and an irrational number can be thought of as multiplying a number that can be expressed as a fraction (rational number) with a number that cannot be expressed as a fraction (irrational number)
The product of a rational number and an irrational number can be thought of as multiplying a number that can be expressed as a fraction (rational number) with a number that cannot be expressed as a fraction (irrational number).
When multiplying a rational number and an irrational number, the result will always be an irrational number.
To see this, let’s consider an example: multiplying the rational number 1/2 with the irrational number √2.
The product of 1/2 and √2 can be calculated as:
(1/2) * (√2)
To simplify this expression, we can multiply the numerators together and multiply the denominators together:
(1 * √2) / (2)
Since √2 cannot be expressed as a fraction, it remains in the numerator. The denominator remains as 2.
So, the product of 1/2 and √2 is (√2) / (2), which is an irrational number.
In general, when you multiply any rational number with any irrational number, the result will always be an irrational number. This is because multiplying an irrational number with any rational number results in an expression where the irrational part cannot be eliminated or simplified to a rational number.
Therefore, the product of a rational number and an irrational number is always an irrational number.
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