## Tuesday, October 26, 2010

### Square Root

Square Root is an inverse of squaring:
The square root of 25 is SxS or what times itself has a product of 25. 5x5=25

Finding the square root using a calculator:

We also learned how to find the square root of a number. From what I've learned so far the only real way to get the square root of a number is to use your trusty old calculator. Of course, each calculator is different, so you may have to punch in a few things before you get the answer.

Let's take the number 3. I know what you're thinking, "but, it's impossible to make a square out of that!" If you remember from last class, it is possible, just a lot less simple to find. So, that's where square root comes in.

Okay then, now punch in the square root function on your calculator and you should get: 1.414213562. Well, that's not a nice number to work with, so let's just take the numbers up to the thousandths place, no rounding please. So, now we should have 1.41.
1.41 x 1.41=1.9881
Not exactly a perfect square, but it's close.

Estimating the square root using fractions:

Remember the number line we made for homework? That would come in handy right about now.

As you can see the space between the two perfect squares is divided into 3. So then we will be using 3 as the denominator for the following fractions. It won't be as exact as the calculator, but it's close.
1: 1
2: 1 1/3
3: 1 2/3
4: 1 3/3 or 2
See how that works? Remember, we won't just use 3 as the denominator. For example the next fraction should be out of 5, since the space between the 2nd perfect square and the 3rd perfect square is divided into 5.

Estimating the square root using perfect squares:

Either the number line or the chart we did would be useful for this activity.

First let's take a number like, 439, and find the square root. Now don't panic, it's a lot easier than you think.
Find on the chart 2 numbers where 439 falls between. It should be 400 and 441.
Next we look on our chart to find the square root or side lengths of both numbers, which would be, 20 and 21. This means the square root of 439 would lie between 20 and 21.
The number can't be 20 or 21 so it should be 1 of those two numbers and a decimal. But which number should be used? 20 of course! If you used 21 and a decimal it would no longer be a number in between the two.
So the answer is 20.___ You don't need the rest, this is an estimation after all.

Now that you know this the homework shouldn't be much of a problem.

Homework:

Use fractions to estimate the square roots of 1-25.
Use perfect squares to estimate the square roots of 200, 37, 850, and 77.

If you're still having trouble with this, here is a site I think you should look at. This probably isn't the best site out there, so leave links to other sites in the comments section and I'll be sure to change it.
Also, here is a video. Also not the best video, so a link or two to another one would be just great.

1. Wonderful post Anabelle ! I really liked how you made the important words stand out ! I kind of forgot about the homework, so thanks for putting it up. I also liked the picture, video and link you put !

2. Great post, Anabelle! The picture of the numberline is clear and easy to understand, and I also liked how you made the important words stand out with only 2 colors, not anymore than that so it wouldn't be distracting. The video and link are quite helpful to me, so thanks for putting that up.

3. Great job Anabelle! Your post was very detailed and neat. I see you used a link, a video, and an image, and that helped me understand your post a lot. I also liked how you highlighted the important words in your post. It made the post both colourful and neat. By the way, it's 'a link of two' not 'a link or too'. Aside from that your post was awesome.

4. A link of two? Do you mean, a link or two? Anyway, I changed it, so thanks for pointing it out for me.

5. Very detailed post Annabelle, I liked that you used the colors to makes some stand out but I think you used it too much.I liked that you explained about the inverse of square and explained it. The part about figuring out the estimate square root is very detailed and also the video, great job.

6. Very great post, Anabelle. It was very detailed and a great explaination. I liked how you picked two colors on your post and reminding us what is our homework for today. The video and pictures helped me alot. Good job.

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8. Good Job! Annabelle. Your work was neat, and you didn't leave anything out. The important things were highlighted in only 2 colours, and I liked that it wouldn't get people distracted. I liked the link, but don't you mean 'a link of two'? i don't know, but it was a really good post! :)

9. Another great post Anabelle! Your post was neat and organized and you explained everything in great detail. I liked how you used colours to emphasize key words and I liked how you didn't go overboard with them. Your post was easy to comprehend and the video and website was very helpful as well. Thanks for putting the homework, I'm sure that was helpful for allot of people. Your post was really good, keep up the good work!

10. You did a great job. One thing I noticed was that when you were talking about the square root function your example was 3 but you ended with 1.41x1.41=1.9881 which is 2 not 3. Anyway I loved the picture that you had and the post was very helpful. I think the estimating will be very as soon as I memorize all the perfect squares and that's not an insult I'm just really bad at estimating. Thanks for the homework and I bet that the link will help people who need it.

11. Awesome post, Anabelle! I really liked how you explained everything. It was really easy to understand. I also like that you had pictures, a link, and a video. I thought you did an awesome job!

12. Great job, Anabelle! You really took your time to add videos. Also it's really colorful and well organized.

13. Great post Anabelle. You explained it really well. I like your picture and the video was helpful. You also colored the important things. Good job and keep up the good work Anabelle.

14. Great post Anabelle. I like how you used only two colours to highlight what's important so it's not that distracting. You explained it very well. Great job. Keep up the good work.