square root - Maple Help

simplify/sqrt

simplify square roots

 Calling Sequence simplify(expr, sqrt) simplify(expr, sqrt, symbolic)

Parameters

 expr - any expression sqrt - literal name; sqrt symbolic - (optional) literal name; symbolic

Description

 • 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).

Examples

 > $\mathrm{simplify}\left({16}^{\frac{3}{2}},\mathrm{sqrt}\right)$
 ${64}$ (1)
 > $\mathrm{simplify}\left({\left(10{x}^{2}+60x+90\right)}^{\frac{1}{2}},\mathrm{sqrt}\right)$
 $\sqrt{{10}}{}{\mathrm{csgn}}{}\left({x}{+}{3}\right){}\left({x}{+}{3}\right)$ (2)
 > $\mathrm{assume}\left(0
 > $\mathrm{simplify}\left({\left(10{x}^{2}+60x+90\right)}^{\frac{1}{2}},\mathrm{sqrt}\right)$
 $\sqrt{{10}}{}\left({\mathrm{x~}}{+}{3}\right)$ (3)
 > $\mathrm{simplify}\left({\left(\frac{90}{121}\right)}^{\frac{1}{2}},\mathrm{sqrt}\right)$
 $\frac{{3}{}\sqrt{{10}}}{{11}}$ (4)
 > $\mathrm{simplify}\left(\sqrt{6}-\sqrt{2}\sqrt{3},\mathrm{sqrt}\right)$
 ${0}$ (5)
 > $f≔{\left(\frac{4{y}^{2}\left(y-x\right){\left(1-\mathrm{Pi}\right)}^{2}}{{\mathrm{Pi}}^{2}{x}^{3}\left(1-E\right)}\right)}^{\frac{1}{2}}$
 ${f}{≔}\sqrt{{4}}{}\sqrt{\frac{{{y}}^{{2}}{}\left({y}{-}{\mathrm{x~}}\right){}{\left({1}{-}{\mathrm{\pi }}\right)}^{{2}}}{{{\mathrm{\pi }}}^{{2}}{}{{\mathrm{x~}}}^{{3}}{}\left({1}{-}{E}\right)}}$ (6)
 > $\mathrm{simplify}\left(f,\mathrm{sqrt}\right)$
 $\frac{{2}{}\left({-}{1}{+}{\mathrm{\pi }}\right){}\sqrt{\frac{\left({-}{y}{+}{\mathrm{x~}}\right){}{{y}}^{{2}}}{{\mathrm{x~}}{}\left({-}{1}{+}{E}\right)}}}{{\mathrm{\pi }}{}{\mathrm{x~}}}$ (7)
 > $\mathrm{simplify}\left({\left({t}^{2}\right)}^{\frac{1}{2}},\mathrm{sqrt}\right)$
 ${\mathrm{csgn}}{}\left({t}\right){}{t}$ (8)
 > $\mathrm{simplify}\left({\left({t}^{2}\right)}^{\frac{1}{2}},\mathrm{sqrt},\mathrm{symbolic}\right)$
 ${t}$ (9)