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No. Sqrt(-4) contains a radical but it not irrational; it is imaginary.
Yes.
√ 5 is an irrational number. Any square root of a prime number is irrational.
No they are not. The numbers Pi and e are irrational and are not radicals. There are many others.
No. 4 over 4, or 1 whole, is not an irrational number. It can be written as a simple fraction, 4/4, so it is not an irrational number.