If p is a perfect square, psqrt returns a square root of p.  Otherwise it returns the name _NOSQRT.

If p is an nth power, proot(p, n) returns a nth root of p.  Otherwise proot returns the name _NOROOT.

$\mathrm{psqrt}\left(9\right)$

$3$

$\mathrm{proot}\left(9\,2\right)$

$3$

$\mathrm{proot}\left(27\,3\right)$

$3$

$\mathrm{psqrt}\left(x^2+2xy+y^2\right)$

$x+y$

$\mathrm{psqrt}\left(9x^2+12xy+4y^2\right)$

$3x+2y$

$\mathrm{proot}\left(x^3+3x^2+3x+1\,3\right)$

$x+1$

$\mathrm{psqrt}\left(x^2-y^2\right)$

$\mathrm{\_NOSQRT}$

$\mathrm{proot}\left(81x^4+108x^3+54x^2+12x+1\,4\right)$

$3x+1$

$\mathrm{psqrt}\left(x+y\right)$

$\mathrm{\_NOSQRT}$

$\mathrm{proot}\left(x+y\,3\right)$

$\mathrm{\_NOROOT}$

$\mathrm{proot}\left(x^3+y^3\,3\right)$

$\mathrm{\_NOROOT}$