## Tia_Sweetheart17 4 years ago square root of 512m^3. show work

1. Rogue

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. $\sqrt{512 m^3} = \sqrt{64 * 8 m^3}$

2. Rogue

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

3. anonymous

256 is also a perfect square factor :)

4. Rogue

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

5. Rogue

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

6. Rogue

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:$\sqrt{512 m^3} = 16\sqrt{2} m^{1.5}$

7. Rogue

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

8. Rogue

Either way, the answer is still the same.

9. anonymous

I assume it's a variable

10. Rogue

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

11. anonymous

lol