Multiply. See Example 7. (√5 + 2)²

Question

Accepted Answer

Hello, everyone. We are asked to simplify the following expression. In parentheses, we have the squared of 13 plus seven closed parentheses squared. Our answer choices are a 13 plus two radical seven B 49 plus radical 13 C 62 plus 14 radical 13 D 13 plus two radical 13. So first, I'm rewriting my expression. So I have the square to 13 plus seven in parentheses squared. And I think for myself, the clearest way to do this is I'm gonna rewrite this as two binomials multiplied together. So I have the square to 13 plus seven in parentheses, multiplied by the square to 13 plus seven in parentheses. I do this so I can use the foil method and I don't have to worry about any shortcuts that I may or may not fully remember. So in foil, we're called F stands for first. So multiplying the first terms of each binomial together, the square to 13 multiplied by the square to 13 is like the square to 13 squared, which will cancel itself out and leave us with outer. We have the square to 13 multiplied by seven, which will be a positive seven radical inner, we have a positive seven multiplied by the square to 13. So we have plus seven radical 13 and last will be seven multiplied by seven, which is 49. So now I'm gonna combine like terms, I recall that a radical is very much like a variable. So if we have the same number under the radical, we can combine the coefficients. So my leg terms here, I have seven radical 13 plus seven radical 13, which would be 14 radical and I have 13 49 that are both constants. So I'm gonna combine those together and we will get 62. So we are left with 62 plus 14 radical 13. And that's the simplification of this expression in its answer choice C have a nice day.

Multiply. See Example 7. (√5 + 2)²

Key Concepts

Binomial Expansion

Square of a Sum

Simplifying Radicals

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