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← Situating Roots of Negatives - College Algebra

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Showing Revision 2 created 05/24/2016 by Udacity Robot.

  1. So, we're interested in exploring the situation where a determinant, b squared
  2. minus 4ac, is negative or less than 0. The reason this is an issue is because we
  3. know we need to take the square root of the determinant, and right now, we have
  4. no idea what taking the square root of a negative number means. None of the
  5. types of numbers we've dealt with so far can express the answer to this
  6. equation. So, I guess that means we're going to need a new kind of number. Let's
  7. look back then at all the kinds of numbers we have dealt with. Here's a diagram
  8. depicting our world of numbers that Julie introduced in the very first lesson of
  9. the course. I know this looks a little bit different because I decided to use
  10. rectangles this time instead of circles, but all the sets and subsets have the
  11. same relationship to one another. You can see that we have the natural numbers,
  12. which are inside of the whole numbers, which are inside of the integers, which
  13. are inside of the rationals. And together, the rationals and the irrational
  14. numbers make up the real numbers. The question I have for you then is where this
  15. new kind of number we're talking about belongs. We see that the number n is some
  16. negative real number. Where should we put the square root of n? Does it belong
  17. in the natural numbers? The whole numbers? The integers? The rationals? The
  18. irrational numbers? Or outside of the real numbers?