Chapter P - Section P.3 - Radicals and Rational Exponents - Exercise Set - Page 48: 139

$4$

Rationalize the denominator of part of the radicand. We have $\frac{7}{3+\sqrt 2}=\frac{7}{3+\sqrt 2}\times\frac{3-\sqrt 2}{3-\sqrt 2}=\frac{21-7\sqrt 2}{9-2}=3-\sqrt 2$. Thus the original expression becomes $\sqrt {13+\sqrt 2+3-\sqrt 2}=\sqrt {16}=4$