sum of rational number and irrational number is
When it comes to adding a rational number and an irrational number, the result is always an irrational number
When it comes to adding a rational number and an irrational number, the result is always an irrational number.
To understand why, let’s start by defining what a rational number is. A rational number is a number that can be expressed as the quotient of two integers, where the denominator is not zero. In other words, it can be written as a fraction.
On the other hand, an irrational number cannot be expressed as a simple fraction or ratio of two integers. Examples of irrational numbers include √2, π, and e.
Now, when we add a rational number and an irrational number, let’s say “a” (rational) and “b” (irrational), we can express the sum as:
a + b
Since “a” is a rational number, it can be written as a fraction:
a = c/d
Where “c” and “d” are integers, and “d” is not zero.
Now let’s substitute this into the sum:
c/d + b
To simplify this expression, we need to obtain a common denominator. However, no matter what denominator we choose, “b” will always remain an irrational number.
Therefore, the sum of a rational number and an irrational number remains an irrational number.
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