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.

(√2 + √7)²

Accepted Answer

Hello, everyone Where the following expression perform multiplication and further simplify if possible. The expression we're given is the quanti radical three plus radical 13 squared. Our answer choices are a 16-plus radical 39 B 178 Plus two radical C16 -2 radical D 178 -2 Radical 39 rewriting this binomial Again, I have open parentheses. Radical 3-plus radical 13 closed parentheses squared. So if you recall when you had a binomial squared, there's a certain pattern to find our answer our trinomial. In this case, our answer is going to simplify all the way down to a binomial. But we're going to use the same steps we would if we were working with variables, recall those steps are the first term comes from squaring. The first term in the binomial. So the square root of three squared would be three. The middle term comes from the product of the two terms in the binomial multiplied by two. So the product of the square to three multiplied by the square to 13 is the square root of Doubled would be Plus two radical 39. And the final term comes from the second term in our binomial squared. So the squared of 13 squared, Which is 13 because the square root in the square offers its and cancel out. Now, I'm gonna combine my like terms I have three and 13 that are both constants. So that adds to 16 Plus two Radical 39. Let's see if there's anything else that can be simplified. Um there is no perfect square that I can take out of 39. So I cannot simplify my radical And I cannot combine any other terms. So this is my solution 16-plus 2 radical 39, which is answer choice a have a nice day.

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

Key Concepts

Radical Expressions

Binomial Expansion

Simplifying Radical Expressions

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