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What is sqrt3(250x^6  simplified?

 Mar 4, 2019
edited by Guest  Mar 4, 2019
 #1
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Is your question supposed to be formatted like this?: (250x^6)^3

 Mar 4, 2019
 #2
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Yes. I couldnt figure out how to make it look like the question on here.

Guest Mar 4, 2019
 #3
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I apologize for not fully understanding your question :/

 

I see your actual question format, but I am unable to help you with this... sorry!

Guest Mar 4, 2019
edited by Guest  Mar 4, 2019
 #4
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\(\sqrt[3]{250x^6}\)

So, in this case, a cube root is the same as that value to the power of 1/3.

\((250x^6)^{\frac{1}{3}}\)

Then, you just multiply the exponents by each other. 

\(6*\frac{1}{3}=\frac{6}{3}=2\)

So that makes it:

\(250x^2\)

.
 Mar 4, 2019
 #5
avatar+23337 
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simplify

\(\mathbf{\large{\sqrt[3]{250x^6}}}\)

 

\(\begin{array}{|rcll|} \hline && \mathbf{\large{\sqrt[3]{250x^6}}} \\ &=& \sqrt[3]{250}\sqrt[3]{x^6} \\ &=& \sqrt[3]{250}\cdot x^{\frac{6}{3}} \\ &=& \sqrt[3]{250}\cdot x^{2} \\ &=& \sqrt[3]{2\cdot125}\cdot x^{2} \\ &=& \sqrt[3]{2}\sqrt[3]{125}\cdot x^{2} \\ &=& \sqrt[3]{2}\sqrt[3]{5^3}\cdot x^{2} \\ &=& \sqrt[3]{2}\cdot 5^{\frac{3}{3}} \cdot x^{2} \\ &=& \sqrt[3]{2}\cdot 5^{1} \cdot x^{2} \\ &\mathbf{=}& \mathbf{\sqrt[3]{2}\cdot 5 \cdot x^{2} } \\ \hline \end{array}\)

 

 

laugh

 Mar 4, 2019

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