Can you add two rational number to get irrational number?

Answer 1

Yes, we can get a rational number on the addition of two Irrational Numbers.

e.g. Let us consider two irrational numbers: 3 + √2 and 4 - √2.

Addition yields:

(3 + √2)+ (4 - √2) = 3 + 4 = 7(a rational number).

Another example is:

Addition of √2 and -√2.

√2+ (-√2) = 0(a rational number).

Explanation of example 1:

Irrational numbers in the form of of p + q are are the irrational numbers which are obtained on addition of two terms: one is rational(p) and another is irrational(q).

And on taking the conjugate of p + q we get p - q, which is an another irrational number. And the addition of these two yields a rational number.

Answer 2

No. By definition, each rational number must be expressible exactly as a ratio of two integers. A common denominator of the denominators of these fractions can always be found by multiplying the two denominators together, and this product will still be an integer. The two original fractions can then be converted to this common denominator by multiplying the numerator of each one by the denominator of the other, again producing only integer products, and adding these two numerator products. This sum divided by the common denominator will be the sum of the original fractions, and, as demonstrated above, its numerator and denominator will both be integers. Therefore, this sum will be rational.