Rationalizing the denominator of [tex]\frac{\sqrt[3]{2z} }{\sqrt[3]{z^2} }[/tex]
we get [tex]\frac{\sqrt[3]{2} }{\sqrt[3]{z} }[/tex].
Option D is correct.
Step-by-step explanation:
We need to rationalize the denominator: [tex]\frac{\sqrt[3]{2z} }{\sqrt[3]{z^2} }[/tex]
Solving:
[tex]\frac{\sqrt[3]{2z} }{\sqrt[3]{z^2} }[/tex]
using Radical rule: [tex]\frac{\sqrt[n]{x}}{\sqrt[n]{y}}=\sqrt[n]{\frac{x}{y} }[/tex]
[tex]=\sqrt[3]{\frac{2z}{z^2}}[/tex]
[tex]=\sqrt[3]{\frac{2}{z^{2-1}}}[/tex]
[tex]=\sqrt[3]{\frac{2}{z^{1}}}[/tex]
[tex]=\sqrt[3]{\frac{2}{z}}[/tex]
We can write it as:
[tex]\frac{\sqrt[3]{2} }{\sqrt[3]{z} }[/tex]
So, rationalizing the denominator of [tex]\frac{\sqrt[3]{2z} }{\sqrt[3]{z^2} }[/tex]
we get [tex]\frac{\sqrt[3]{2} }{\sqrt[3]{z} }[/tex].
Option D is correct.
Keywords: Radical Expression
Learn more about Radical Expression at:
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brainly.com/question/7153188
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