yes
Such a sum is always rational.
yes
No. Two irrational numbers can be added to be rational. For example, 1/3 + 2/3 = 3/3. 1/3 and 2/3 are both irrational, but 3/3 = 1, which is rational.
Because no two integer numbers divide to make the number "square root of 7".
yes
In general, no. It is possible though. (2pi)/pi is rational. pi2/pi is irrational. The ratio of two rationals numbers is always rational and the ratio of a rational and an irrational is always irrational.
it is not irrational. This is because there are two non irrational numbers that divide each other that are rational. So 10.46 is rational.
Since the sum of two rational numbers is rational, the answer will be the same as for the sum of an irrational and a single rational number. It is always irrational.
They are always rational.
Such a sum is always rational.
Not necessarily. The sum of two irrational numbers can be rational or irrational.
No. The square root of two is an irrational number. If you multiply the square root of two by the square root of two, you get two which is a rational number.
yes
No. In fact, the sum of conjugate irrational numbers is always rational.For example, 2 + sqrt(3) and 2 - sqrt(3) are both irrational, but their sum is 4, which is rational.
No. sqrt(3) - sqrt(2) is irrational.
No. Two irrational numbers can be added to be rational. For example, 1/3 + 2/3 = 3/3. 1/3 and 2/3 are both irrational, but 3/3 = 1, which is rational.