sum of rational number and irrational number is
irrational
The sum of a rational number and an irrational number is an irrational number.
To prove this, let’s assume that we have a rational number ‘a’ and an irrational number ‘b’. Then the sum of a and b is:
a + b
Since a is a rational number, we can express it as a fraction of two integers p and q, where q is not equal to zero.
a = p/q, where p and q are integers and q is not equal to zero.
Now let’s substitute the value of a in the original equation:
a + b = p/q + b
Since b is irrational, we cannot express it as a fraction of two integers. Therefore, we cannot combine p/q and b into a common fraction. Thus, a + b cannot be reduced to a rational number and is irrational.
Therefore, the sum of a rational number and an irrational number is an irrational number.
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