Grades 11-12 Video Solutions 2021-video 2021 11-12/2

Video Transcription

Problem number two states, how many integers are in the open interval from 20 minus root 21 to 20 plus root 21?  So we're going to have an interval surrounding 20 with either side that stretches length of root 21 on both sides. So let's figure out just how big root 21 is.  So root 21 will be bigger than root 16, yet smaller than root 25. We know this since root 16 is 4 and root 25 is 5. So root 12 will be 4 point something.  Keeping this in mind, let's take a look at our interval. So here we have the number line surrounding 20.  And we know that our interval stretches root 21 below 20 and root 21 above 20. So that means at the lower bound we will get 15 point something and for the upper bound  we will get 24 point something. This means all these numbers in the middle are in our interval.  The numbers 16, 17, 18, 19, 20, 21, 22, 23, and 24 are all the integers in the interval and we have nine numbers.  So the question asked us, how many integers are in the interval from 20 minus root 21 to 20 plus root 21? The answer is 9, letter E.

Video Summary

The problem involves finding integers in the open interval from \(20 - \sqrt{21}\) to \(20 + \sqrt{21}\). Estimating \(\sqrt{21}\) as between 4 and 5, the interval spans from approximately 15 to 25. Therefore, the integers within this interval are 16, 17, 18, 19, 20, 21, 22, 23, and 24. The total number of integers is 9.