Multiply. See Example 7. (√2 + 1) (√3 + 1)

Question

Accepted Answer

Hello, everyone. We are asked to simplify the following expression. The expression we are given is the parentheses, the square root of three plus four closed parentheses, multiplied by the parentheses, the square rod of five plus four closed parentheses. Our answer choices are a, the square to 15 plus four radical three plus four radical five plus 16 B seven radical five plus four radical three plus C three radical 15 plus five radical three plus two radical five plus 16 D, the square of 15 plus 16. I'm gonna begin by rewriting our expression. So we have a parentheses, the square of three plus four closed parentheses, multiplied by the parentheses, the square of five plus four closed parentheses. Looking at this, I have the product of two binomials. So I'm gonna use the foil method. Recall that foil stands for first, outer, inner, last. And that's the order I'm gonna be multiplying in. So first, we have the squared of three multiplied by the squared of five. Since they are both square roots, we can multiply them together and keep them under a radical sign or a square root symbol. And they'll give us radical 15 or the squared of outer, we have the squared of three multiplied by four. Here, since four is not under a square root, we cannot combine them, but we can write them next to each other. So we'll have plus four radical three inner would be four multiplied by the square of five. And again, we can't combine them because four is not under a radical, but we can write them next to each other if you will as multiplication. So we have plus four radical five and then last, we have four multiplied by four, which is 16. Looking to see if anything else can be reduced or combined. I noticed the square to 15, there is no perfect square to factor out there. Uh the square to three and the square to five cannot be combined as they are different. So this is as factored as this gets, we're gonna be as simplified as we can here. So we have the square to 15 plus four radical three plus four radical five plus 16. And that's answer choice. A have a nice day.

Multiply. See Example 7. (√2 + 1) (√3 + 1)

Key Concepts

Binomial Multiplication

Simplification of Radicals

Combining Like Terms

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