Sometimes.
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The square of a rational number can be either rational or irrational. However, the square of an irrational number is always irrational.
The square root of 2 is irrational, yet the product of it with itself is 2. So the answer is no.
Sometimes. eg the irrational number √2 squared is 2 which is rational (2 = 2/1) eg the irrational number √(√2) squared is √2 which is irrational.
No. The square root of an integer is always either an integer or an irrational number.
It is a irrational number. Because the square root of every imperfect square is irrational number.
It is not! The square root of 2, for example, is irrational but you can always locate it exactly by using the diagonal of a unit square.