# Why is this happening? (simple)

1. May 8, 2013

### cdux

Please let me understand this conceptually:

Why is the square root of 400 20 times smaller than 400, but the square root of 40 is not 20 times smaller than 40?

It may sound simple to say "because square root of X is not linear" but my main question is, why/how does that translate to physical laws and different units?

For example why is it right to say Y = square root of X when for an X in 4 meters the result would be 2 but for an X in 0,004 killometers it would be 0,006324.. kilometers!?

Last edited: May 8, 2013
2. May 8, 2013

### Stephen Tashi

Did you mean to say "20 times smaller than 40"?

3. May 8, 2013

### pwsnafu

Do you mean 0.0632? (one zero after the decimal not two?)

Edit:
$\sqrt{0.004} = \sqrt{4 \times 10^{-3}} = 2 \sqrt{10^{-3}}$

Notice that if we had $\sqrt{0.04} = \sqrt{4 \times 10^{-2}} = 0.2$

10 squared gives 100 not 1000, but 1 kilometer = 1000 meters.

4. May 8, 2013

### cdux

Dang I just realized why. I didn't square the kilo. lol.