Chapter 7 - Section 7.5 - Multiplying with More Than One Term and Rationalizing Denominators - Exercise Set - Page 549: 15

$117-36\sqrt{7}$

Use the FOIL method, with $\sqrt{a^{2}}=(\sqrt{a})^{2}=a$ (for positive a). $F:\quad 6\times 2=12$ $O:\quad 6\times(-5\sqrt{7})=-30\sqrt{7}$ $I:\quad -3\sqrt{7}\times 2=-6\sqrt{7}$ $L:\quad -3\sqrt{7}\times(-5\sqrt{7})=+15(\sqrt{7})^{2}=15\times 7=105$ Add like terms: (F+L)+(O+I) $...$= $117-36\sqrt{7}$