CONCEPT PREVIEW Perform the operations mentally, and write the an...

Question

CONCEPT PREVIEW Perform the operations mentally, and write the answers without doing intermediate steps.

(√28 - √14) (√28 + √14)

Accepted Answer

Welcome back. I am so glad you're here. We're asked to perform the operation without the use of a calculator. Our expression is the quantity of the square rut of 45 minus the square rut of 22 multiplied by the quantity of the square of 45 plus the square of 22. Our answer choices are answer choice. A the square rut of 23 answer choice B 23 answer choice, C 1541 and answer choice D 32. All right. So there are a couple of ways that we could go about solving this. The first is we could use the foil process multiplying the firsts from each set of parentheses, then multiplying the outsides from each set of parentheses, then multiplying the insides from each set of parentheses and then multiplying the lasts from each set of parentheses, then combining like terms and simplifying. However, there's actually another way we can solve this one and I think this one's pretty neat looking at what's inside of the parentheses. We have the same number in both slots at the beginning of both sets of parentheses and the same number in the second spot in both sets of parentheses. And this looks a lot like a difference of squares factored out. We recall from previous lessons that once we factored out a difference of squares that is open parentheses, A minus B closed parentheses multiplied by open parentheses. A plus B closed parentheses. And yeah, we can say that our, a term here is the square root of 45. We can say that the B term here is the square rut of 22. 1 set of parentheses has subtraction and one set has addition. So this is a difference of squares, which is great because once we foil that out, we know that it's going to equal A squared plus, excuse me, difference of A squared minus B squared. We know what A is and we know what B is. So we can plug those in A is the square ret of 45. We'll need to square that. And then subtract B is the square rot of which we also need to square. Well, the square rut of 45 squared is just 45. Then we bring down subtraction and the square rot of squared is just and 45 minus 22 is a positive 23. And there is our answer simplified. We look at our answer choices and this matches with answer choice B well done. We'll catch you on the next one.

CONCEPT PREVIEW Perform the operations mentally, and write the answers without doing intermediate steps. (√28 - √14) (√28 + √14)

Key Concepts

Difference of Squares

Square Roots

Simplification of Radicals

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