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.
  ____________
√1² − 4 ⋅ 0.5 ⋅ 5

Accepted Answer

Welcome back everyone. In this problem, we want to simplify the expression of the square root of two squared minus eight, multiplied by 0.25 multiplied by 20. And we want to express our answer in standard form for our answer choices A is negative two multiplied by the square root of 11 IB is two multiplied by the square root of 11 IC is negative six I and D is six. I. Now, what do we know here? We're trying to simplify our expression and put it in standard form. And that's the standard form for complex numbers. Recall that for a complex number, writing it in standard form means that we're putting it in the form A plus B I where A is a real number and B is the imaginary number. And we'll need to do that because we're finding the square root of what may become a negative value. And whenever we are finding the square root of a negative value, by definition, the imaginary unit I equals the square root of negative one. So let's see that let's let's work out what we already have here. Try to simplify and see if it becomes a negative value. No, two squared is four and eight multiplied by 0.25. That's eight multiplied by a quarter, which is two. And we're going to multiply that by 20 two multiplied by 20 equals 44 minus 40 equals negative 36. So yeah, we're going to have to find the square root of a negative number. No, I need to factor negative one out of my term. So that means I can rewrite it as the square root of multiplied by negative one. Now, this is pretty helpful because what we know about radicals, we can also recall that the radical of a product A B equals the radical of A multiplied by the radical of B. So applying that idea, we can rewrite our expression even further as the square root of 36 multiplied by the square root of negative one. By definition, I equals the square root of negative one and the square of 36 equals six. So my final answer would have been six. I and we know it's in standard form because even though there's no real part, it's showing an imaginary part. Therefore, our final answer would be answer choice. D thanks a lot for watching everyone. I hope this video helped.

In Exercises 29–36, simplify and write the result in standard form. ____________ √1² − 4 ⋅ 0.5 ⋅ 5

Key Concepts

Square Root

Standard Form

Quadratic Expression

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