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# simplify

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5 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 :/

Guest Mar 4, 2019
edited by Guest  Mar 4, 2019
#4
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$$\sqrt{250x^6}$$

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
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simplify

$$\mathbf{\large{\sqrt{250x^6}}}$$

$$\begin{array}{|rcll|} \hline && \mathbf{\large{\sqrt{250x^6}}} \\ &=& \sqrt{250}\sqrt{x^6} \\ &=& \sqrt{250}\cdot x^{\frac{6}{3}} \\ &=& \sqrt{250}\cdot x^{2} \\ &=& \sqrt{2\cdot125}\cdot x^{2} \\ &=& \sqrt{2}\sqrt{125}\cdot x^{2} \\ &=& \sqrt{2}\sqrt{5^3}\cdot x^{2} \\ &=& \sqrt{2}\cdot 5^{\frac{3}{3}} \cdot x^{2} \\ &=& \sqrt{2}\cdot 5^{1} \cdot x^{2} \\ &\mathbf{=}& \mathbf{\sqrt{2}\cdot 5 \cdot x^{2} } \\ \hline \end{array}$$ Mar 4, 2019