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

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

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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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we're solving for the quantity of three plus Route five a B cubed, the quantity squared. So I'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'm going to use foil first outside, inside last to expand even further. It's almost ply the first numbers together. I'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'm actually going to make sure that this doesn'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'll just be the number that'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.

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