No. It is an irrational number and so cannot have a repeating decimal representation (or in any other rational base).
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You take a guess as to an approximate square root, for example 2, which is the square root of 2. You divide 5 by 2, to get 2.5. The real square root will be between 2 and 2.5, so you take the average of these two (2.25). You divide 5 by 2.25 to get the next approximation. Repeat a few times, until you have the desired accuracy.
No, an irrational number is, in simple terms, a number that keeps repeating. The square root of 4 is positive or negative 2, which does not repeat and is therefore rational.
2 square root 2
21.447610589527216 (does not repeat to 20 places)
the square root of 4 is 2 square root 2