there is a number x such that x^2 is irrational but x^4 is rational justify your answer by an example
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yes there are so many no. example 2^(1/4) which is irrational and its square is 2^(1/2) which is also irrational but again squaring it becomes 2 which is rational no.
Note: If a no. is rational then its square is always rational.
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