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In $3-41$ , express each product in simplest form. Variables in the radicand with an even index are non-negative.$$-\sqrt{10} \cdot \sqrt{18}$$

$-6 \sqrt{5}$

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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 $3-41$ , express each p…

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for this problem we need to solve for the negative square root of 10 times the square root of 18. In order to do this, we need to keep in mind that the square root of any number a times the square root of another number B is equal to the square root of their product or the square root of a times B. In our original expression, this means that we have negative square root of 10 times 18 10 times 18 is 180 leaving us with the negative square root of 180. We can't stop here. We need to break it down. We're gonna use the opposite where we're gonna go in reverse off this principle that we used earlier. So we need to think what to numbers multiply together to create 180. We have a punch. We have a few different options. We could use nine times 20. We could use 36 times five. We could even use 10 times 18 But that would just get us back to where we started. So the one that I'm gonna use is 36 times five. So from here we'll get negative. Route 1 80 is equal to negative root. 36 times five. I'm gonna bring my expression down to another line. We need to separate these out into different radical signs. So this is equal to negative. Route 36 times. Route five simplifying even further. This negative 36 negative. Route 36 is equal to a whole number. Actually, the root of 36 is six. So we have just negative six from that negative route 36 times the square root of five. This leaves us with our final answer of negative six, Route five.

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