Why is this happening? (simple)

[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!?

 

[Stephen Tashi]

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

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

 

[pwsnafu]

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!?

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.

 

[cdux]

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

Abandon ship! Abandon thread!