The function rationalize attempts to rationalize the given expression, removing all roots from the denominator.

rationalize does not operate inside transcendental functions, such as exp and sin. Radical expressions that are arguments to such functions within expr will not be rationalized.

$\mathrm{rationalize}\left(\frac{2}{2-\mathrm{sqrt}\left(2\right)}\right)$

$2+\sqrt{2}$

$\mathrm{rationalize}\left(\frac{1+2^{\frac{1}{3}}}{1-2^{\frac{1}{3}}}\right)$

$-\left(1+2^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}\right)\left(2^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}+2^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}+1\right)$

$\mathrm{rationalize}\left(\frac{x+y}{\mathrm{sqrt}\left(x+y\right)-1}\right)$

$\frac{\left(1+\sqrt{x+y}\right)\left(x+y\right)}{-1+x+y}$

$\left[\frac{x}{x+\mathrm{sqrt}\left(3\right)}\,\frac{x}{x+\mathrm{sqrt}\left(1+\mathrm{sqrt}\left(3\right)\right)}\,\frac{x+y}{xy+\mathrm{sqrt}\left(3\right)+\mathrm{sqrt}\left(7\right)}\right]$

$\left[\frac{x}{x+\sqrt{3}}\,\frac{x}{x+\sqrt{1+\sqrt{3}}}\,\frac{x+y}{xy+\sqrt{3}+\sqrt{7}}\right]$

$\mathrm{rationalize}\left(\right)$

$\left[-\frac{\left(-x+\sqrt{3}\right)x}{x^2-3}\,-\frac{\left(-x+\sqrt{1+\sqrt{3}}\right)\left(x^2+\sqrt{3}-1\right)x}{x^4-2x^2-2}\,\frac{\left(-xy+\sqrt{7}-\sqrt{3}\right)\left(-x^2{y}^2+2\sqrt{3}xy+4\right)\left(x+y\right)}{x^4{y}^4-20x^2{y}^2+16}\right]$

$\left[\frac{x+y}{x+\mathrm{sqrt}\left(y\right)}\,\frac{xy}{x+\mathrm{sqrt}\left(x+\mathrm{sqrt}\left(3\right)\right)}\right]$

$\left[\frac{x+y}{x+\sqrt{y}}\,\frac{xy}{x+\sqrt{x+\sqrt{3}}}\right]$

$\mathrm{rationalize}\left(\right)$

$\left[-\frac{\left(-x+\sqrt{y}\right)\left(x+y\right)}{x^2-y}\,-\frac{\left(-x+\sqrt{x+\sqrt{3}}\right)\left(x^2+\sqrt{3}-x\right)xy}{x^4-2x^3+x^2-3}\right]$

$\left[\frac{1}{\exp \left(\mathrm{sqrt}\left(x\right)\right)}\,\frac{x+y}{\cos \left(\mathrm{sqrt}\left(x\right)\right)+\sin \left(\mathrm{sqrt}\left(y\right)\right)}\right]$

$\left[\frac{1}{{\ⅇ}^{\sqrt{x}}}\,\frac{x+y}{\cos \left(\sqrt{x}\right)+\sin \left(\sqrt{y}\right)}\right]$

$\mathrm{rationalize}\left(\right)$

$\left[\frac{1}{{\ⅇ}^{\sqrt{x}}}\,\frac{x+y}{\cos \left(\sqrt{x}\right)+\sin \left(\sqrt{y}\right)}\right]$

$\mathrm{rationalize}\left(\frac{1}{1+\mathrm{root}\left(\sin \left(\frac{1}{1-\mathrm{sqrt}\left(\mathrm{\eta }\right)}\right)\,3\right)}\right)$

$\frac{{\sin \left(\frac{1}{1-\sqrt{\mathrm{\eta }}}\right)}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}-{\sin \left(\frac{1}{1-\sqrt{\mathrm{\eta }}}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}+1}{1+\sin \left(\frac{1}{1-\sqrt{\mathrm{\eta }}}\right)}$

$\mathrm{rationalize}\left(\frac{1}{1+{\left(\frac{1}{1-\mathrm{sqrt}\left(a\right)}\right)}^{\frac{1}{3}}}\right)$

$\frac{\left({\left(-\frac{1}{-1+\sqrt{a}}\right)}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}-{\left(-\frac{1}{-1+\sqrt{a}}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}+1\right)\left(-1+\sqrt{a}\right)\left(2+\sqrt{a}\right)}{-4+a}$