simplify/sqrt
simplify square roots
Calling Sequence
Parameters
Description
Examples
simplify(expr, sqrt)
simplify(expr, sqrt, symbolic)
expr
-
any expression
sqrt
literal name; sqrt
symbolic
(optional) literal name; symbolic
The simplify/sqrt function is used to simplify expressions which contain square roots or powers of square roots.
It extracts any square integer or polynomial factor from inside the square root.
The positive square root is used.
You can also apply sqrt(x^2); ==> csgn(x)*x or sqrt(x^2); ==> signum(x)*x if x is known to be real.
Dependent roots like sqrt(6), sqrt(2), sqrt(3) are transformed into having only sqrt(2) and sqrt(3) so as to achieve a normal form.
When the symbolic option is specified, square roots are computed without regard for possible complex or negative values of variables. No csgn() or signum() appears in the answer. The purpose of this feature is to allow simplification of expressions in contexts where the sign has no meaning, such as when x is an algebraic indeterminate. In particular, simplify( sqrt( x^2 - 2*x*y + y^2), sqrt, symbolic), returns at random either x−y or y−x. Furthermore, there is no guarantee that the choice is the same as that made by sqrt( x^2 - 2*x*y + y^2, symbolic).
simplify1632,sqrt
64
simplify10x2+60x+9012,sqrt
10csgnx+3x+3
assume0<x
10x~+3
simplify9012112,sqrt
31011
simplifysqrt6−sqrt2sqrt3,sqrt
0
f≔4π2x3y2y−x1−E1−π212
f≔4y2y−x~1−π2π2x~31−E
simplifyf,sqrt
2−1+π−y+x~y2x~−1+Eπx~
simplifyt212,sqrt
csgntt
simplifyt212,sqrt,symbolic
t
See Also
assume
csgn
radnormal
simplify[radical]
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