Answer
$24 - 6\sqrt{3}$
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:
$=\sqrt{6}(4\sqrt{6}) -\sqrt{6} \cdot 3\sqrt{2}$
Use rule (2) above to obtain:
$=4\sqrt{36} - 3\sqrt{12}
\\=4\sqrt{6^2} - 3\sqrt{4(3)}
\\=4\sqrt{6^2} - 3\sqrt{2^2(3)}$
Simplify each radical to obtain:
$=4(6) - 3(2)\sqrt{3}
\\=24 - 6\sqrt{3}$
