In Exercises 29–36, simplify and write the result in standard for...

Question

In Exercises 29–36, simplify and write the result in standard form.

√(1^2 - 4 × 0.5 × 5)

Accepted Answer

Welcome back. I'm so glad you're here. We have got this big number here and we're going to express it in standard form. So let me rewrite it. We've got the square root of three squared minus nine times one third Times 15. There's a lot going on in there. So we want to recall from previous lessons our order of operations are pem da's acronym which tells us to start with parentheses and exponents and then multiplication and division from left to right, then addition and subtraction from left to right. This whole square root is kind of acting like a parentheses. It means do this stuff inside here first. So there aren't any parentheses inside of there. Now we'll start off with exponents. There is an exponent. This three squared. So let's go ahead and do that. Three squared is going to be nine. So we've got nine minus nine times one third times 15. Inside that square root. Okay, exponents are done there anymore in there now we can do multiplication and division from left to right. The first multiplication we have is negative nine times one third. So we've got the square root of nine and negative nine times one third is negative three. Bring down that times 15. And anymore multiplication or division from left right. Yes this negative three times 15. So we can go ahead and bring down that square root of nine and negative three times 15 in minus 45. Now there's no more multiplication or division in there. Just addition and subtraction. Well subtraction. So we can go ahead and do nine minus that gives us the square root of negative 36. Cool, well we think back to what we're going for here and we're supposed to express this answer in standard form meaning when we've got a square root of a negative number, we've got a complex number. And the standard form for complex numbers is A plus B. I. Or in other words we want to express this in terms of I and I is the square root of negative one. So we've definitely got a negative number inside of our square root bracket. Let's express that in terms of I we can think of this as the squared of not just negative 36 but the squared of negative one times 36. And there we clearly see our square root of negative one which can be rewritten as an eye in front of the square root bracket. Just leaving that squirt of 36 in there. But we know that the square root of 36 is six. So we can now rewrite this as six. I. And that is as simplified as it's going to get. It's in standard form and we can look at our answer choices and it matches with answer choice. D Well done. We'll catch on the next one

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