in-3-41-express-each-product-in-simplest-form-variables-in-the-radicand-with-an-even-index-are-no-37

Question

In $3-41$ , express each product in simplest form. Variables in the radicand with an even index are non-negative.
$$
\left(3+\sqrt{5 a b^{3}}\right)^{2}
$$

Sarah Wharton · Accepted Answer

we&#x27;re solving for the quantity of three plus Route five a B cubed, the quantity squared. So I&#x27;m going to write this out to make it a little bit a little bit easier to solve all. Rewrite it as three plus Route five A. Be cute times three plus Route five A. Be cute, and now I&#x27;m going to use foil first outside, inside last to expand even further. It&#x27;s almost ply the first numbers together. I&#x27;ll read it on the second line as three times three is nine plus the outside numbers that would be three times Route five a B cubed. So three Route five A B cubed plus the inside numbers being multiplied together. That would be three. Route five a. B cubed again, and I&#x27;m actually going to make sure that this doesn&#x27;t look like a cubed root. It looks like a proper coefficients of three. Route five a B cubed. Do that on the other one to just to be clear. And then finally the last. So Route 5 80 cubed times, Route five A B cube. Anything times itself. If both of them are in a square root sign, it&#x27;ll just be the number that&#x27;s inside. So plus five A. Be cute. Now, finally, we need to combine like terms these two in the middle Since they have the same term inside the route, we just have to combine the coefficients, the three and the three. So this is going to be equal to nine plus three plus three is six. So six Route five A B cubed plus five a b cute. And that is our final answer.

Sarah Wharton · Answer

for this problem, we&#x27;re solving three Route three squared, which can be expanded as three route three times three, Route three. To solve this, we multiplied together the whole numbers in front and we multiply the numbers inside the radical signs. So this will be equal to three times three times route three times Route three. This part, the three times three is equal to nine. And the second part here could be combined in the same radical as the square root of three times three. Bringing this down to another line. This is equal to nine times the square root of nine. We know that this word of nine is equal three. So this is equal to nine times three, which is equal to 27 that is our final answer.

Sarah Wharton · Answer

in this question, we&#x27;re going to use foil to solve a plus ruby times a minus ruby foil, meaning first outside inside last, so I&#x27;ll start with the 1st 8 times A. This is equal to a squared. Plus the outside comes next. A times negative root be. Don&#x27;t forget that negative sign, so it&#x27;s going to be a negative a route B. Now comes the inside root. Be times a so B plus a route to be finally, the last part. Positive ruby times and negative root be which will be a negative root. Be Times route. Be so it&#x27;s just negative be continuing to solve. We could notice that negative. A ruby and a ruby just cancel each other out, so our final answer will simply be a squared minus B.

M S · Answer

So we want to simplify this ex question. So the first thing I notice is that we have ah b squared over here. So this is too baby times to route a. So the square root of B squared so the square root in squared will cancel each other out. So we&#x27;ll have to route a ruby times three routing times. So nothing on Edison&#x27;s. We have this to a here and a Subaru a here. So two times he will give us four. And spirit of a town square Today will give us a and you live with the time to spirit be now because we have the same base here. We could simple far this further there is that I have for a be transferred of the

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

so we want to simplify this expression. So this is really related to route by times negative to route by. So negative two times negative to give us positive for. And I swear to box on swearing Bible give us five and four times five. Give us 20.

Problem

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

Problem 39 Hard Difficulty

In $3-41$ , express each product in simplest form. Variables in the radicand with an even index are non-negative.
$$
\left(3+\sqrt{5 a b^{3}}\right)^{2}
$$

Answer

$9+6 b \sqrt{5 a b}+5 a b^{3}$

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$9+6 b \sqrt{5 a b}+5 a b^{3}$

Algebra 2 and Trigonometry

Ann Xavier GantertAlgebra 2 and Trigonometry

Ann Xavier Gantert

Algebra 2 and Trigonometry