Answer
$32 + 11\sqrt{2}$
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,
$\sqrt{a} \cdot \sqrt{b}=\sqrt{ab}$
(3) $(a+b)(c+d) = a(c+d) + b(c+d)$
Use rule (3) above to obtain:
$=5(6+\sqrt{2})+ \sqrt{2}(6+\sqrt{2})$
Use rules (1) and (2) above then simplify to obtain:
$=5(6) + 5\sqrt{2} + \sqrt{2}(6) + \sqrt{2}(\sqrt{2})
\\=30 + 5\sqrt{2} + 6\sqrt{2}+\sqrt{2(2)}
\\=30 + (5+6)\sqrt{2} + \sqrt{4}
\\=30 + 11\sqrt{2} + 2
\\=32 + 11\sqrt{2}$
