Yes the square root of 2 is a surd which is an irrational number that can't be expressed as a fraction.
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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
Expressed as a surd, the square root of 28 is equal to 2 root 7.
That is the only way to write it exactly.
Yes.
There's no reason why it should be, it's 2, end of story.