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

Question

Accepted Answer

Hello, everyone. We are asked to simplify the following expression. We have the parentheses squared of 11 plus the square of five, multiplied by the parentheses, the squared of 11 minus the square of five. Our answer choices are a, the squared of six B six C 11 minus two radical D 25 minus two radical rewriting our expression again, we have the parentheses and then the squared of 11 plus the square of five closed parentheses multiplied by the next set of parentheses, which is the square of 11 minus the square to five. I notice in rewriting this, that I have the product of a sum and a difference which means I have a shortcut I can use. Now, if you don't recall that shortcut, you absolutely could use foil, you will get the same answer. So this is the product of a sum and a difference because they have the same terms but have different signs in between them. So when we have the product of a sum and a difference, we can square the first term in both of our sets of parentheses. So the first term is the squared of 11. So we're gonna do the squared of 11 squared and then we square the last term. So it's the squared of five squared. And our answer is called the difference of squares. So we'll be putting a minus sign in between them. So right now I have the square root of 11 squared minus the square root of five squared. So when I simplify this, the squared of 11 squared leaves me with 11 because a square and a square root will cancel out minus the square root of five squared. And again, the square and the square root cancel out. So I'm left with five and then I do 11 minus five is six. So when we simplify this expression, we get answer choice B six have a nice day.

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

Key Concepts

Difference of Squares

Radicals

Simplifying Expressions

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