[Math] the square root of 1 cm

arithmetic

If $1$cm = $.01$m then shouldn't the square root of $1$cm = the square root of $.01$m
but the square root of $1$ = $1$ while the square root of $0.01$ = $0.1$
So my dilemma, is the square root of $1$ centimeter = $0.01$ meters or $0.1$ meters?

Best Answer

I think you need to think of the square root of a distance as a new unit. Just as a ${m^2}$ is an area, not a distance. So the following works:

$\sqrt {1m} = \sqrt {100cm} $

$\sqrt m = 10\sqrt {cm} $

$\sqrt {1cm} = \sqrt {cm} $

and

$\sqrt {.01m} = .1\sqrt m = .1\left( {10\sqrt {cm} } \right) = \sqrt {cm} $

So it works out either way.

Related Question