Chapter 7 - Section 7.5 - Multiplying with More Than One Term and Rationalizing Denominators - Exercise Set - Page 549: 16

$77-31\sqrt{7}$

Use the FOIL method, with $\sqrt{a^{2}}=(\sqrt{a})^{2}=a$ (for positive a). $F:\quad 7\times 5=35$ $O:\quad 7\times(-3\sqrt{7})=-21\sqrt{7}$ $I:\quad -2\sqrt{7}\times 5=-10\sqrt{7}$ $L:\quad -2\sqrt{7}\times(-3\sqrt{7})=+6(\sqrt{7})^{2}=6\times 7=42$ Add like terms: (F+L)+(O+I) $...$= $77-31\sqrt{7}$