If by "radical" you mean "square root of", then yes.
Both square roots of 25 are real numbers.
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Sqrt(25) is -5 or +5, both of which are rational.
Sure. √6 , the square root of 6, is approximately 2.44949. It's an irrational number --you can't get it as the ratio of any two integers -- but it's real. See Can_a_real_number_be_an_irrational_number
No, it is not.
square root of 125= 25 times 5 under the radical (25 has a square root so you can take that out of the radical)= 5 times the square root of 5 (Thats your final answer with no calculator)
Yes well at least that is what is what ive learnt