## k_lynn one year ago http://prntscr.com/866akv Simplify...

1. mathstudent55

Assuming all variables are non-negative. $$\large \sqrt{200xyz^3}$$

2. anonymous

10 sqrt(2) x y z^3

3. Michele_Laino

hint: $\Large 200 = 2 \cdot 100 = 2 \cdot 4 \cdot 25 = 2 \cdot {\left( {2 \cdot 5} \right)^2}$

4. mathstudent55

$$\large \sqrt{200xyz^3}$$ $$\large = \sqrt{2 \times 100xyz^2z}$$

5. k_lynn

I'm not understanding any of that :/

6. mathstudent55

$$\sqrt{100} = 10$$ and $$\sqrt {z^2} = z$$

7. k_lynn

$2z \sqrt{10xyz}$ Would it be this then?

8. mathstudent55

When you simplify a square root, you need to break up the numbers and variables inside the root into products in which one factor is a square.

9. mathstudent55

$$\large =10z\sqrt{2xyz}$$

10. mathstudent55

You're on the right track, but it's the 10 that comes out and the 2 is left inside.

11. k_lynn

ohh so $10z \sqrt{2xyz}$

12. mathstudent55

Yes.

13. k_lynn

Okie doke. Thanks!

14. mathstudent55

For example, we broke up 200 into 2 * 100. 100 is the largest factor of 200 that is a perfect square.

15. mathstudent55

You're welcome.