k_lynn
  • k_lynn
http://prntscr.com/866akv Simplify...
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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mathstudent55
  • mathstudent55
Assuming all variables are non-negative. \(\large \sqrt{200xyz^3} \)
anonymous
  • anonymous
10 sqrt(2) x y z^3
Michele_Laino
  • Michele_Laino
hint: \[\Large 200 = 2 \cdot 100 = 2 \cdot 4 \cdot 25 = 2 \cdot {\left( {2 \cdot 5} \right)^2}\]

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mathstudent55
  • mathstudent55
\(\large \sqrt{200xyz^3} \) \( \large = \sqrt{2 \times 100xyz^2z} \)
k_lynn
  • k_lynn
I'm not understanding any of that :/
mathstudent55
  • mathstudent55
\(\sqrt{100} = 10\) and \(\sqrt {z^2} = z\)
k_lynn
  • k_lynn
\[2z \sqrt{10xyz}\] Would it be this then?
mathstudent55
  • 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.
mathstudent55
  • mathstudent55
\(\large =10z\sqrt{2xyz} \)
mathstudent55
  • mathstudent55
You're on the right track, but it's the 10 that comes out and the 2 is left inside.
k_lynn
  • k_lynn
ohh so \[10z \sqrt{2xyz}\]
mathstudent55
  • mathstudent55
Yes.
k_lynn
  • k_lynn
Okie doke. Thanks!
mathstudent55
  • mathstudent55
For example, we broke up 200 into 2 * 100. 100 is the largest factor of 200 that is a perfect square.
mathstudent55
  • mathstudent55
You're welcome.

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