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The Compleat User RPL Encyclopedia


(“Square Root”)

z    √z
Keyboard Access (all models): the key.

Square Root analytic function.

Minor warning: On the HP49/50 in exact mode,  calculates the exact square root of integers, that is, it merely places the input under a radical and simplifies it if possible. If is then applied, the final result can be LESS ACURATE than if you had first performed  and then taken the square root. Example (must be in exact mode!):

8      2.82842712474 (last digit is wrong)
8      2.82842712475 (all digits are correct)
(same result as 8.  in exact mode, or 8  in approx mode)
This is not a bug; it is the result of snowballing roundoff error, since the first example requires two calculations ( and ) but the latter only requires one ( ). The error, if any, is only in the last decimal place, by the way, so you probably will not need to worry about it in practical applications.

Second warning: The HP49/50 in exact mode attempts to find the exact result of the square root of an integer, which involves factoring the input, so it can take a very long time for large inputs. Example: 50000017 50000021 takes over 90 seconds on an HP50g just to put the radical symbol over the number since it takes that long to determine that it is has a square-free factorization. The HP Prime performs the same task in less than 0.1 seconds!

HP49/50 maximum integer input: no limit (but see above paragraph; huge integers not easily factored take a very long time).

 also works on units. Example: 9_ft^2     3_ft

 also works on complex numbers. Example:
(3,4)     (2,1)
SQ    (3,4)

See also:

BYTES: 2.5