The type(expr, radnum) function checks to see if expr is a radical number.

A radical number is defined as either a rational number or I, or a combination of roots of rational numbers specified in terms of radicals. A sum, product, or quotient of these is also a radical number.

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

$\mathrm{true}$

$\mathrm{type}\left(\ln \left(2\right)\,\mathrm{radnum}\right)$

$\mathrm{false}$

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

$\mathrm{true}$

$\mathrm{type}\left(\frac{5}{\mathrm{sqrt}\left(2\right)}\,\mathrm{radnum}\right)$

$\mathrm{true}$

$\mathrm{type}\left({\left(\frac{3}{2}\right)}^{\frac{4}{3}}\,\mathrm{radnum}\right)$

$\mathrm{true}$

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

$\mathrm{false}$