Chapter R - Section R.8 - nth Roots; Rational Exponents - R.8 Assess Your Understanding - Page 79: 54

$\displaystyle \frac{\sqrt{2}(\sqrt{7}-2)}{3}=\frac{\sqrt{14}-2\sqrt{2}}{3}$

We rationalize the denominator: $\displaystyle \frac{\sqrt{2}}{\sqrt{7}+2}=\frac{\sqrt{2}(\sqrt{7}-2)}{(\sqrt{7}+2)(\sqrt{7}-2)}=\frac{\sqrt{2}(\sqrt{7}-2)}{7-4}=\frac{\sqrt{2}(\sqrt{7}-2)}{3}=\frac{\sqrt{14}-2\sqrt{2}}{3}$