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!

 

[CellCoree]

The square root of a number is the number that, when multiplied by itself, gives the original number. In the case of the square root of 400, it is 20 because 20 x 20 = 400. However, when we look at the square root of 40, it is not 20 times smaller than 40 because the square root is not a linear function. This means that the relationship between the input number (X) and the output number (Y) is not a straight line.

In the example given, the units of measurement (meters and kilometers) also play a role in the difference between the square root of 4 and the square root of 0.004. This is because the units are not directly comparable.

The square root of a number is a mathematical concept that is used to find the length of one side of a square with a given area. It is important to understand that this concept is purely mathematical and does not necessarily translate directly to physical laws or units. The relationship between X and Y in the square root function is based on the mathematical properties of the function, not on physical laws.

In summary, the square root of a number is not linear because it is a mathematical concept, and the relationship between the input and output is not a straight line. The difference in units also plays a role in the difference between the square root of 400 and the square root of 40. It is important to understand the difference between mathematical concepts and physical laws when trying to understand these concepts.