It turns out, that orbit is the square root of 27 times just a handful of fundamental constants.

结果是，轨道是27倍于少数基本常数的平方根。

And so this is 49 square roots of 3 newtons out of the surface, out of the surface.

这个力，也就是平行於斜面的这个地心引力的分力这个力，也就是平行於斜面的这个地心引力的分力。

For example, for a long time, there was no such thing as taking the square root of negative numbers.

例如，长期以来，负数是不能取平方根的。

And one cried, " Can you show me how to extract this square root" ?

！ 有人喊道，“你能告诉我如何提取这个平方根吗” ？

Take the square roots of both sides.

取两边的平方根。

You look at the other possible options for numbers you could take the square root of.

你看看其他可能的数字选项，你可以取平方根。

So you add 7 to get to 9, then take the square root again.

所以你加 7 得到 9，然后再次取平方根。

So it's 200 times the square root of 3 over 2, which equals 100 square root of 3.

所以它是 3 的平方根乘以 2 的 200 倍，等于 3 的 100 平方根。

What's going to be the square root of that?

它的平方根是多少？

I just took the square root of both sides of this equation.

我只是取了这个等式两边的平方根。

And if you take its square root for the standard deviation, which is what we do right here, it's 0.49.

如果你用它的平方根来表示标准偏差，这就是我们在这里所做的， 它是 0. 49。

And if you wanted the standard deviation of this distribution right here, you just take the square root of both sides.

如果你想要这个分布的标准偏差就在这里，你只需取两边的平方根。

But then mathematicians defined the square root of negative one as a new number called i, opening up a whole new mathematical world of complex numbers.

但后来数学家们取 -1 的平方根为一个叫 i 的新数字，在数学领域里，这为复杂数字打开了全新的世界。

My sample standard deviation is just going to be the square root of my sample variance.

我的样本标准差只是样本方差的平方根。

You're taking the square root of both sides.

你正在取两边的平方根。

And if I want to figure out my sample standard deviation I just take the square root of that.

如果我想计算出我的样本标准偏差，我只需对其求平方根。

And you want to take a square root of the right-hand side just like that.

你想像这样对右边求平方根。

So I take the square root of that value that I just had, which is 0.497.

所以我取我刚刚得到的值的平方根，即 0.497。

Standard error would be the square root of this.

标准误差将是这个的平方根。

In that case, multiplying by that number twice would be the same as multiplying by 3, which means the multiplier would be the square root of 3.

这样的话，乘这个数两次，就等于原本的数量乘以 3，那这个乘数就应该是根号 3。