In Exercises 1–38, multiply as indicated. If possible, simplify a...

Question

In Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product.(7 + √2) (8 + √2)

Accepted Answer

Hello, everyone. For the following expression perform multiplication and simplify if possible. The expression we are given is the Quan D 13 plus radical 11 multiplied by the quan D 17 plus radical 11. Our answer choices are th A plus 30 radical 11. B 232 plus 30 radical C 342 plus 221 radical D 232 Plus 221 Radical 11. Rewriting my original binomials again, I have the Quan 13 plus radical multiplied by the Kandi 17 Plus Radical 11. And I'm gonna treat this just like I would. If this was any other binomial, I'm gonna go through it using foil and then once I'm done using foil, I'll clean up what I can with my radical rules. So foil first. So the first terms multiplied together 13 multiplied by 17. That results in outer 13 multiplied by radical 11. This is very much like if I had done 13, multiplied by X, the 13 stays on the outside. The radical 11 does not change. So we have plus 13 radical 11 in radical 11 multiplied by 17, which again, I can't combine them in any way other than writing them next to each other. So I get 17 radical 11 and last radical 11 multiplied by radical 11. Again, recall when we have the square root symbols, we keep the symbol, the radical symbol, we can multiply what is underneath. So 11 multiplied by 11 is 11 squared. I'm writing it like that on purpose. So it makes it a little easier to simplify. So currently I have 221 plus 13 radical 11 plus 17 radical 11 plus the square root of 11 squared. I'm going to simplify what I can Keeping My 221. Next, I have like radicals in the 13 radical 11 and 17 radical 11. So I'm gonna add their coefficients to get 30 radical and then simplifying that last term, which is the square root of 11 squared. We'll write that as plus 11 because a square root will cancel out a square. We have one last set of like terms here. We can combine our 221 and our 11. She will give us plus 30 radical 11 and that is our solution. It matches answer choice B have a nice day.

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In Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product.(7 + √2) (8 + √2)

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