The type(expr, radext) function checks if expr is a radical extension of the real numbers.  It is equivalent to type(expr, radical) or $\mathrm{expr}=\mathrm{I}$.

The type(expr, radext(K)) function checks whether expr is a radical expression where the expression under the root sign belongs to the domain K.  For example, K could be integer or rational.

This function returns true if expr is such an expression. Otherwise, false is returned.

$\mathrm{type}\left(\mathrm{sqrt}\left(x^2+5\right)\,\mathrm{radext}\right)$

$\mathrm{true}$

$\mathrm{type}\left({\left(x^2+5\right)}^{\frac{4}{3}}\,\mathrm{radext}\left(\mathrm{polynom}\right)\right)$

$\mathrm{true}$

$\mathrm{type}\left(5-{\left(\mathrm{sqrt}\left(3\right)\right)}^{\frac{5}{6}}\,\mathrm{radext}\left(\mathrm{rational}\right)\right)$

$\mathrm{false}$

$\mathrm{type}\left({\left(5-\mathrm{sqrt}\left(3\right)\right)}^{\frac{5}{6}}\,\mathrm{radext}\left(\mathrm{radnum}\right)\right)$

$\mathrm{true}$

$\mathrm{type}\left(\frac{2}{3}\,\mathrm{radext}\right)$

$\mathrm{false}$