sum of rational number and irrational number is
when you add a rational number and an irrational number, the resulting sum will be an irrational number
when you add a rational number and an irrational number, the resulting sum will be an irrational number.
To understand why, let’s first define what a rational number and an irrational number are.
A rational number is any number that can be expressed as a fraction, where the numerator and denominator are integers, and the denominator is not zero. For example, 1/2, -3/4, and 5 are all rational numbers.
On the other hand, an irrational number is a number that cannot be expressed as a fraction. They are non-repeating and non-terminating decimals. Some common examples of irrational numbers include π (pi), √2 (square root of 2), and e (Euler’s number).
Now, let’s consider adding a rational number to an irrational number. Let’s say we have the rational number 1/2 (which can be expressed as a fraction) and the irrational number √2 (which cannot be expressed as a fraction). When we add these two numbers, we get:
1/2 + √2
Since √2 cannot be written as a fraction, we cannot combine the terms into a single fraction. Therefore, the sum 1/2 + √2 remains as an irrational number.
In general, when you add any rational number to any irrational number, the result will always be an irrational number. This is because the addition of a decimal number that repeats or terminates (rational number) with a decimal number that does not repeat or terminate (irrational number) will always result in a non-repeating and non-terminating decimal, which is characteristic of irrational numbers.
So, the sum of a rational number and an irrational number is always an irrational number.
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