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.
No. All irrational numbers are real, not all real numbers are irrational.
Every irrational number is a real number.
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.