Square roots

[sxk1693]

I'v begin to notice that a lot of questions have been asking me to do things like truncating sqrt(4) + sqrt(5) to the third decimal place. To what number and how many decimal places should I memorize square roots to. Also How Would You Do These:

2^2 + 81^2
How many scalene acute triangles have integer sides with all sides less than or equal to 4.
I know I should know this by now but how do you find the number of distinct diagonals of a regular polygon.

Finally, tell me if I am doing this right:
Find the sum of the coefficients of the binomial expansion of(7y-4y)^3.
(7-4)^3 = 27

[PokémonMaster]

First of all, yes, you are doing the sum of coefficients right.

Square roots are supposed to be memorized up to 10, i think. Just the first 3 decimal places sould be enough.

2^2 + 81^2, just foil 81^2 if you don't know it, and add 2^2, which you should know is four.

Distinct diagonals in a regular polygon is s(s-3)/2, where s is the number of sides. As for the triangle one... I have no idea. :P

[nsguy1350]

[unparseable or potentially dangerous latex formula]. It's the outside add up to 10, second is one greater than third trick.
I just crunched though, knowing that [unparseable or potentially dangerous latex formula].

Umm... scalene is the key:
123 - not a triangle
124 - not a triangle
134 - not a triangle
234 - not acute

Should be zero. I think I put that when I took the test.

Distinct diagonals is also (n-2)th triangular number - 1, where n is the number of sides.

And yes, PokemonMaster was right when he said that you were correct.

[FabensMath]

How do you know which ones make triangles?

[PokémonMaster]

[nsguy1350]

Think about it this way:

Have a line segment a, and two other line segments b and c such that a = b+c.
The only possible arrangement of these is to have b and c be parallel, touching at the endpoints, and touching the endpoints of a. This is not defined as a triangle, since it's basically a line segment with two line segments overlapping it.

To make a triangle, b and c must be connected at an angle < 180 degrees, and that increases their length.
You cannot connect a line segment with two other ones that sum to less than that lien segment if you want each line segment to connect to the two others, forming a triangle.

[murali0298]

Just wondering...
How do you get those pictures on the side?
I tried it on that avatar thing but it says that the url is too long.
How long is it supposed to be?