in-3-41-express-each-product-in-simplest-form-variables-in-the-radicand-with-an-even-index-are-non-5

Question

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

Sarah Wharton · Accepted Answer

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&#x27;t stop here. We need to break it down. We&#x27;re gonna use the opposite where we&#x27;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&#x27;m gonna use is 36 times five. So from here we&#x27;ll get negative. Route 1 80 is equal to negative root. 36 times five. I&#x27;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.

M S · Answer

so we want to simplify through two times routine. So San does not have any factors that are perfect squares. But we do know that a factor of 10 is too. And we do see a two already. In our expression, we can break apart spirit of 10 and to swear to it sounds very five. And the reason I picked two and five was because we have this route to here in this room, too. That was already in our expression. So now we can have three times greater to Times Square in two will begin bliss to and some scoring five and three times to give us six and bring down a starting spot.

M S · Answer

So we have to square in 21 something spirit of 4/3. So one thing I noticed automatically is that if we split apart our second square root, so have a scary to four. On top of spirit of three, we can simplify our numerator. But I also noticed that three is a factor. 21 focus put apart our 21 We have skirted three times square to seven. So I&#x27;m screwed of four over square 23 Another square root of four is too. So we have three times. We&#x27;re seven times to over Route three. And since the rules applying, we can cancel this out with our three on the bottom, they&#x27;ll have to say I was a spirit of seven.

M S · Answer

so I have the spirit of eight times the square root of 12. So if you want to simplify this, that really means you want to think about the factors of each number and factor out the part picks were said backers of eight. You have won eight in two and four and our four is the perfect where so we know that the square root of four is too. Now come in handy. In a second, we have someone do something with our 12. So think about the factors of 12 will have warning spoiled to in six and three and four. But we also have this perfect square here, bored So we&#x27;ll separate both of them. Those good of apes. We wouldn&#x27;t have that story before. And four times to gives us a and to separate our square root of 12. We&#x27;ll have our spirit before, and four times three is 12. So we can simplify straight for is to and every necessary to and story for again is to bring down this very three Sanam. Just wanna, since everything is multiplied almost wanna multiply our regular numbers so two times Cygnus four and they will still have the spirited suits on spirit of three. And we can simplify under that radical sometimes three who did this

Sarah Wharton · Answer

for this problem we&#x27;re trying to solve for the square root of two times the square root of eight, and I&#x27;m problems like these. We need to keep in mind that the square root of any number, for example, a times the square root of another number, for example, B is always equal to the square root of their product or the square root of a times B. So the squared of two times the square to eight is equal to then. The square root of two times eight two times eight is 16 so this expression is equal to the square root of 16 squared of 16 could be simplified to equal for. Therefore, the answer. This question is for

M S · Answer

So you have this very look love times one minus spirit of 10. So in distribute this group five So we have scary five times when I was just worried by minus one day, we have skirted five times greater so we can go on borrowing. They used to have to be on the same radical. So have a lot of time. Sam wishing it was 50. So let&#x27;s think about the practice of 50. We have one in 50 soon 25 and five and 10. Well, I see a perfect square here. 25 is a perfect square. Was scary to 25 this far. So we want to split apart. Are scared of Sin City This would be square to 25 sounds great and scary. 25 is five and just bring down the spirits.

Problem

In $3-41$ , express each product in simplest form…

Problem 7 Medium Difficulty

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

Answer

$-6 \sqrt{5}$

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$-6 \sqrt{5}$

Algebra 2 and Trigonometry

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Ann Xavier Gantert

Algebra 2 and Trigonometry