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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.
phi = [1+sqrt(5)]/2 sqrt(5) is irrational and so phi is irrational.
It is an irrational number. Actually it is a rational number. Think 2/3=.6666666, 1/9=.11111111.
The square root of 2 is irrational, yet the product of it with itself is 2. So the answer is no.
irrational