The square root of any positive, non-square number will be both real and irrational.
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All real numbers are irrational. For example, Pi is an irrational number that is a real number. Other irrational numbers can be the square root of an imperfect square.
Every irrational number is a real number.
No. All irrational numbers are real, not all real numbers are irrational.
No. The square root of negative one is an example of an imaginary (not real) number. Pi is irrational, but real.
No, because it could be a rational number.