Nailing Square Root operations - any links/PDF's

[Bang!Zoom!]

Just that one topic.  Nailing square root math functions.  Any suggestions?

[wapiti]

Nail prime factorization first?

 

See, e.g., the following AoPS videos:

 

 

 

Chapter 9: Square Roots back to top

• Section 9.1: Square Root Introduction Part 1
• Section 9.1: Square Root Introduction Part 2
• Section 9.2: Non-Integer Square Roots
• Section 9.3: Square Root of a Product
• Section 9.3: Sum of Square Roots
• Section 9.3: Simplifying Square Roots Part 1
• Section 9.3: Simplifying Square Roots Part 2

 

[regentrude]

What "square root operations" are you referring to? Taking the square root of a number that is not, on first glance, identifiable as a perfect square? Or taking the square root of algebraic expressions?

[Bang!Zoom!]

Wapti, I used those links and those are a good start point.  

 

Regentrude, I've been seeing different types of square roots talked about beyond single digit positive or perfect.  This is for me to learn, so those AoPS are going to be a good place for me to start.

 

I am stuck on one thing though on what I'm trying to finish, and that is the "why" of the formula on a unit circle at the 270 degree mark.  The formula is 3pi/2 - I get all the other ones except that one.  (insert three year old whiny voice..)

 

Why is it 3pi over 2?  WwwwhhhHHy? :confused1: 

 

What is the relationship there?  I'll attack it all again tomorrow.  I have the circle memorized, everything makes sense except that one right there.

 

 

 

 

 

 

[Arcadia]

 

I am stuck on one thing though on what I'm trying to finish, and that is the "why" of the formula on a unit circle at the 270 degree mark.  The formula is 3pi/2 - I get all the other ones except that one.  (insert three year old whiny voice..)

 

Why is it 3pi over 2?  WwwwhhhHHy? :confused1: 

This?

 

"

• Convert 270° to radians.

Since 180° equates to π, then:

The equivalent angle is  "

[regentrude]

I am stuck on one thing though on what I'm trying to finish, and that is the "why" of the formula on a unit circle at the 270 degree mark.  The formula is 3pi/2 - I get all the other ones except that one.  (insert three year old whiny voice..)

 

Why is it 3pi over 2?  WwwwhhhHHy? :confused1:

Are you familiar with the angle notation in radians?

Let's cut a piece of circle, like a pizza piece, angle theta wide, radius of the circle is R. The round portion of the outside rim of the piece has some length s. Now of course, the bigger the pizza, the bigger R and the bigger s, but if the angle is the same, the ratio of s/r will not change, because that only depends on what angle the pizza piece is. R and s both grow with the same factor as the pizza circle is enlarged.

We are defining the angle in radians as simply the arc length s divided by the radius: theta in radians = s/R

 

Now let's think: if you have the entire pizza, i.e. a 360 degree angle, how long is the rim? It is one circumference: s=2 pi R.

So, the angle 360 degrees in radians equals s/R=( 2pi R)/R = 2 pi

360 degrees equals 2 pi radians.

 

Now if you have a quarter pizza, i.e. 90 degrees - that's a quarter of 2 pi = pi/2

And 270 degree is three quarters of 360 degrees, so 270 degrees = 2* pi radians* 3/4= 3*pi/2 radians

 

Since radians is not "really" a unit (length divided by length has no dimension), it is often simply omitted, and we say 270 degrees=3 pi/2

Hope this helps.

[kiana]

I am stuck on one thing though on what I'm trying to finish, and that is the "why" of the formula on a unit circle at the 270 degree mark.  The formula is 3pi/2 - I get all the other ones except that one.  (insert three year old whiny voice..)

 

Why is it 3pi over 2?  WwwwhhhHHy? :confused1: 

 

What is the relationship there?  I'll attack it all again tomorrow.  I have the circle memorized, everything makes sense except that one right there.

 

Hum. Do you mean "Why is 270 degrees equivalent to 3pi/2?"

 

If you understand that 90 degrees is pi/2, and that 180 degrees is pi, then you just need to add them up. 180 + 90 = 270, and pi + pi/2 = pi (1 + 1/2) = pi (3/2). If you prefer it in words, you could say that a whole pi plus a half pi equals one and a half pi which is three half-pi. (And the best thing about that is that it also works with pies!)

 

[Bang!Zoom!]

I think I get it...thank you.

 

Everything on the circle made complete sense but that one, it seemed somehow out of pattern with no reason...but I get it now.  I think there was something about the 3/4/6 pattern that was throwing me off, even though it was in an entirely different spot for function.

 

The explanation helped a lot!  Thanks!

 

I'm absolutely amazed at how rigid my mind seems to be with this stuff, I have to work 25x harder than the kid does at getting it and keeping it.  Tomorrow I will start squares, it'll probably take me a week with constant review to learn it.

[Soror]

I'm absolutely amazed at how rigid my mind seems to be with this stuff, I have to work 25x harder than the kid does at getting it and keeping it.  Tomorrow I will start squares, it'll probably take me a week with constant review to learn it.

Lol, this is my life right now w/ grammar! It does provide me w/ a lot more patience in teaching and determination to give him a better education than I received.