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In $3-41$ , express each product in simplest form. Variables in the radicand with an even index are non-negative.$$(9+\sqrt{2 b})(1+\sqrt{2 b})$$

$9+10 \sqrt{2 b}+2 b$

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Chapter 3

REAL NUMBERS AND RADICALS

Section 5

Multiplying Radicals

Whole which of Numbers

Fractions and Mixed Numbers

Decimals

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in this problem, we're going to use foil to solve nine plus route to be times one plus route to be starting with the F for first nine times, one is equal to nine, so that will be our first term in the expansion up. Next comes the outside numbers nine times route to be We'll have plus nine route to be, plus the inside term one times route to be one route to be, plus the last route to be times route to be, which we can combine in one radical as route to be times to be. This could be simplified further as nine plus, recognizing that these two are like terms because they both have the route to be so. We nine plus 10 from the nine plus one route to be plus square root of two times two is four b times B is B squared. This four B squared can be broken down into root for times Route B squared. This in turn, is equal to two from the root. For times, be so really square root of for B Squared is just to be meaning that our final answer will be nine plus 10 route to be plus to be

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