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.
Sometimes it is and sometimes it isn't. The square root of 2 and the square root of 3 are both irrational, as is their product, the square root of 6. The square root of 2 and the square root of 8 are...
Yes.
An example:
1 + 2^(0.5) is an irrational number,
1 -(2^(0.5)) is also a irrational number.
(1 + 2^(0.5)) + (1- 2^(0.5)) = 2
2 is a rational number.
Therefore the sum of two irrational numbers...