Because the opposite of 8 for example is -8 and 8+(-8) = 0
When the number is non-positive.
Yes, it will always be irrational.
Think of a numberline, Travle 5 sides to the negative side, and than 5 steps back , this is negative 5 and positive 5. This appplies for all rational numbers
The product of 0 and an irrational is 0 (a rational), the product of a non-zero rational and any irrational is always irrational.
Only if the rational number is 0.
When the number is 0.
the number 0 is always equal to its opposite
When the number is non-positive.
No. If the rational number is not zero, then such a product is irrational.
Yes, always.
The answer depends on whether the "opposite" means the multiplicative inverse or the additive inverse.
Yes, it will always be irrational.
Think of a numberline, Travle 5 sides to the negative side, and than 5 steps back , this is negative 5 and positive 5. This appplies for all rational numbers
Yes, except in the degenerate case where the rational number is 0, in which case the product is also 0, a rational result.
The product of 0 and an irrational is 0 (a rational), the product of a non-zero rational and any irrational is always irrational.
Only if the rational number is 0.
No, never.