in-3-41-express-each-product-in-simplest-form-variables-in-the-radicand-with-an-even-index-are-no-24

Question

In $3-41$ , express each product in simplest form. Variables in the radicand with an even index are non-negative.
$$
\sqrt{5}(1-\sqrt{10})
$$

M S · Accepted 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.

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 one place 35 times three minus the square root of. So this is sort of like oiling little ball of the same pattern. So the first time supper. So we have one times three. Would you give this three outer scare the bottoms? One who could give those straight of five. But it&#x27;s negative. So minus required. The owner turns took place three times, scary to five. And then finally, the last turn the cause of times and I need it will give us a negative and a spirit if eyes on the skirt five because they&#x27;re the same, it&#x27;s just not again a spot that radical counsel&#x27;s out and there are a lot of super can simplify further and we can So we have three and negative 53 minus spot would give us needed to You will have negative to Lina scurrying by loose three different spots. And if you notice we have the same radical here and here and this isn&#x27;t understood one here. So we can combine these two so have negative too. And negative Born plus three will give us two So negative two planets to Route five. All I did was combined the coefficient here. Anna coefficient Here, get radical. Listen departed

M S · Answer

Some have to square 258 times square to buy they minus three. So because we have parentheses here and distribute So this times this and because they&#x27;re the same the radical just cancel out. So we just have five a and I will multiply. This times are three. So have minus three times is very 58 and us, as far as you&#x27;ve been simplified it.

M S · Answer

way have the square root of Bob. I&#x27;m scared of 45. We want to express this in simplest terms. The birth. I&#x27;m gonna say to square toe five time. We&#x27;re gonna break apart this query. 45. So think about the factors of 45 we have one and 45 in five and nine, so I see a perfect square here. Nine is three squares. That means that the square root of nine is three. So because we have that perfect split here, we want to separate this and say square to nine Times square in five. Just weakened back throughout that were fixed. Where there So spirit of nine is three and we still have a skirt of five times 35. It&#x27;s very defiant. Some square to five will give us by. There are three times five and begins this 15

Sarah Wharton · 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.

Problem

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

Problem 26 Easy Difficulty

In $3-41$ , express each product in simplest form. Variables in the radicand with an even index are non-negative.
$$
\sqrt{5}(1-\sqrt{10})
$$

Answer

$\sqrt{5}-5 \sqrt{2}$

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$\sqrt{5}-5 \sqrt{2}$

Algebra 2 and Trigonometry

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