# Chapter 10 - Radical Expressions and Equations - 10-3 Operations with Radial Expressions - Practice and Problem-Solving Exercises - Page 617: 43

x = $9+3 \sqrt 10 + 6 \sqrt 2 + 2 \sqrt 20$

#### Work Step by Step

$\frac{2 + \sqrt 2}{2 + \sqrt 2} = \frac{x}{3 + \sqrt 10}$ We cross multiply the fraction $\frac{(2 + \sqrt 2)(3 + \sqrt 10)}{2 + \sqrt 2} = x$ We simplify the top by using FOIL. FOIL: First (Multiply the first variables in the brackets), outside (Multiply the outer variables), Inside (Multiply the inside variables), Last (Multiply the last variables in the brackets). $\frac{6 + 3\sqrt 2 + 2\sqrt 10 + \sqrt 20}{2 + \sqrt 2}$ = x We simplify the denominator and numerator. $x = (3)(3) + (3)(\sqrt 10) + (6)(\sqrt 2) + 2(\sqrt 20)$ We add the radicals with the same numbers and the constants together x = $9+3 \sqrt 10 + 6 \sqrt 2 + 2 \sqrt 20$

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