product of rational number and irrational number is
When you multiply a rational number and an irrational number, the result will always be an irrational number
When you multiply a rational number and an irrational number, the result will always be an irrational number. This is because the product of a rational number (which can be expressed as a fraction) and an irrational number (which cannot be expressed as a fraction) will not be able to simplify or reduce to a rational number.
To understand this concept, let’s consider an example:
Let’s multiply the rational number 3/4 with the irrational number √2.
(3/4) * √2 = (3/4) * (√2)
To compute this multiplication, we can rationalize the denominator by multiplying the numerator and denominator by √2.
(3/4) * (√2) * (√2/√2) = (3/4) * (√2 * √2) / (√2)
Simplifying this expression gives us:
(3/4) * (2) / (√2)
Multiplying the numerators and denominators:
(3 * 2) / (4 * √2)
Simplifying further:
6 / (4√2)
We can simplify this expression by dividing both the numerator and denominator by 2:
3 / (2√2)
As you can see, the result of multiplying a rational number (3/4) with an irrational number (√2) is an expression that cannot be reduced further. Therefore, the product of a rational number and an irrational number is always an irrational number.
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