+0

simplify

0
33
5

What is sqrt3(250x^6  simplified?

Mar 4, 2019
edited by Guest  Mar 4, 2019

#1
0

Is your question supposed to be formatted like this?: (250x^6)^3

Mar 4, 2019
#2
0

Yes. I couldnt figure out how to make it look like the question on here.

Guest Mar 4, 2019
#3
0

I apologize for not fully understanding your question :/

Guest Mar 4, 2019
edited by Guest  Mar 4, 2019
#4
+10
0

$$\sqrt[3]{250x^6}$$

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
+21848
+1

simplify

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

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

Mar 4, 2019