Question

square root of 512m^3. show work

Answer 1

Radicals... In order to find the square root, we need to find a perfect square factor of 512. 64 is a perfect square factor, which can be multiplied by 8 to give 512. So we can write the square of 512 this way.
\[\sqrt{512 m^3} = \sqrt{64 * 8 m^3}\]

Answer 2

\[\sqrt{64}*\sqrt{8 m^3} = 8 * \sqrt{4 * 2 m^3}\]

Answer 3

256 is also a perfect square factor :)

Answer 4

\[8*\sqrt{4}*\sqrt{2 m^3} = 8*2*\sqrt{2 m^3} = 16\sqrt{2m^3}\]

Answer 5

Yeah, we could've skipped all that using 256, thanks Rick :)

Answer 6

The cube root of meters cubed is meters to the 1.5 power (yeah, I know, its weird). So you can write your final answer as:\[\sqrt{512 m^3} = 16\sqrt{2} m^{1.5}\]

Answer 7

Well, is that meters cubed, or is it a variable?

Answer 8

Either way, the answer is still the same.

Answer 9

I assume it's a variable

Answer 10

Yeah, makes more sense, meters to the 1.5 power, lol.

Answer 11

lol