The type(expr, radnumext) calling sequence checks to see if expr is a radical number extension.

A radical number extension is an algebraic number extension specified in terms of radicals. This is a root of a combination of rational numbers and roots of rational numbers specified in terms of radicals.

The type(expr, radnumext) calling sequence is equivalent to type(expr, radnum) and (type(expr, radext).

$\mathrm{type}\left({\left(-1\right)}^{\frac{1}{2}}\,\mathrm{radnumext}\right)$

$\mathrm{true}$

$\mathrm{type}\left({\left(\mathrm{sqrt}\left(5\right)-\frac{3}{2}\right)}^{\frac{4}{3}}\,\mathrm{radnumext}\right)$

$\mathrm{true}$

$\mathrm{type}\left({\left(4-5^{\frac{1}{3}}\right)}^{\frac{1}{4}}\,\mathrm{radnumext}\right)$

$\mathrm{true}$

$\mathrm{type}\left(x^{\frac{1}{4}}\,\mathrm{radnumext}\right)$

$\mathrm{false}$

$\mathrm{type}\left(\mathrm{I}\,\mathrm{radnumext}\right)$

$\mathrm{true}$