Memorize the basic square roots..ie of 3 and 2. Sq rt of 3 is 1.732 and div by 2 is app 0.8. 5*0.8 is 4. Hence answer is around 400,000.

Estimating should be sufficient. 500,000/2 = 250,000. You know that √4 is 2 and √2 is 1.4, so √3 is somewhere in between. So you answer should be somewhere in the middle of 500000 to 375000 (I round 1.4 to 1.5 because its easier to do in the head).

Do it like this. 500,000 = 5 x 10^5, √3 = 1.7 (these you just have to memorize: √2 = 1.4, and √3 = 1.7). So we have 500,000 * ((√3)/(2)) = (5 x 10^5) * (1.7/2). Since 5/2 = 2.5, we have: (2.5 x 10^5)*(1.7) = (25 x 10^-1 x 10^5)*(17 x 10^-1) = (25 x 17)*(10^3) At this point, you could either estimate the answer to be ~ 20 x 20 * 10^3 ~ 400,000 (remember if you choose to round 17 up to 20, you should probably round the other number 25 down to balance it, so you don't overestimate the answer). Or, it's simple enough to actually multiply out 25 x 17 = 425, so the more exact answer is 425,000.

whoa, keep it simple guys. dont complicate it more than it is memorize these 2, it's easy sqrt 3 = 1.7 sqrt 2 = 1.4 500,000 * (sqrt 3 / 2) 500,000 * (1.7 / 2) 500,000 * ~0.9 answer: 450,000 (exact answer is 433012.70....)

root 3 and root 2 might as well be memorized as then it makes projectile motion a lot quicker too.... so if you know that root 3 over 2 is 0.85 and root 2 over two is 0.7 you will save you're self a bit if it comes up.

Bingo. That is probably the fastest way to estimate that problem. Remember to keep in mind whether your estimations will overestimate or underestimate your answer. Here, Asuka estimated that 1.7/2 = .9, but really 1.7/2 is smaller than .9 That means that the answer will be slightly less than 450,000.

Taylor series.... (I got to plug them twice in one day oh boy) http://forums.studentdoctor.net/showpost.php?p=6802401&postcount=6 Using a very simple approximation, you would get sqrt(3) ~ 1.75 where the actual value is 1.732...