# Chapter 8 - Section 8.3 - Operations with Radicals - Exercise Set - Page 592: 51

$32+11\sqrt{2}$

#### Work Step by Step

RECALL: Two binomials can be multiplied using the formula: $(a+b)(c+d) = a(c+d) + b(c+d)=ac+ad+bc+bd$ The last expression, $ac+ad+bc+bd$, is what others refer to as the FOIL method of multiplying two binomials (the sum of the products of: First terms, Outer terms, Inner terms, and Last terms) Use the formula above to obtain: $=5(6)+5\sqrt{2}+6\sqrt{2}+\sqrt{2}\cdot\sqrt{2} \\=30+(5\sqrt{2}+6\sqrt{2})+\sqrt{4} \\=30+(5\sqrt{2}+6\sqrt{2})+2$ Simplify to obtain: $=(30+2)+(5+6)\sqrt{2} \\=32+11\sqrt{2}$

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