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

$2 \sqrt{2}+2$

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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 question, we're solving for the square root of two times the quantity of two plus route to. To do so will be using the distributive property showing here where we distribute this route to OutFront to both of the terms. Inside the parentheses, we'll get route to times two, plus a route to times route to this will give us to root. Two rewritten toe have the whole number Elton front, plus the square root of two times to. Because any two routes multiplied together, we can just multiply them in one big route, so this will be equal to to root two plus the square root of four, which is just equal to to root two plus two.

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