## Intermediate Algebra for College Students (7th Edition)

$58 + 15\sqrt{2}$
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: $=7(8+\sqrt{2})+ \sqrt{2}(8+\sqrt{2})$ Use rules (1) and (2) above then simplify to obtain: $=7(8) + 7\sqrt{2} + \sqrt{2}(8) + \sqrt{2}(\sqrt{2}) \\=56 + 7\sqrt{2} + 8\sqrt{2}+\sqrt{2(2)} \\=56 + (7+8)\sqrt{2} + \sqrt{4} \\=56 + 15\sqrt{2} + 2 \\=58 + 15\sqrt{2}$