No. Surds are a type of real number. Infinity is not a real number.
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A surd is an irrational number that can't be expressed as a fraction as for example the square root of 2
Yes the square root of 2 is a surd which is an irrational number that can't be expressed as a fraction.
It is impossible to have a surd that is not irrational. Surds are defined to be an irrational number (square root of a number).
Yes.