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.
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.
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.