Answer
$7\sqrt{6} - 6$
Work Step by Step
RECALL:
(1) Distributive Property:
For any real numbers a, b, and c,
$a(b-c) = ab - ac$
(2) For any real numbers real numbers a and b within the domain,
$\sqrt[n]{a} \cdot \sqrt[n]{b} = \sqrt[n]{ab}$
(3) $\sqrt{a} \cdot \sqrt{a} = a, a \ge 0$
Use rule (1) above to obtain:
$=\sqrt{6} \cdot 7 - \sqrt{6} \cdot \sqrt{6}
\\=7\sqrt{6} - \sqrt{6} \cdot \sqrt{6}$
Use rule (3) above to obtain:
$=7\sqrt{6} - 6$
