perform the indicated operation [tex] \sqrt{2 \div } \sqrt[3]{?} 2[/tex]. Created by stacybudz. Math

Answer:Is that correct? Or is that supposed to be Radicals are basically exponents in fraction form. That's means:From there you basically have:OR...There you have it. Just continue solving it and you have your answer.

tex]...

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stacybudz @stacybudz

October 2022 1 4 Report

perform the indicated operation
[tex] \sqrt{2 \div } \sqrt[3]{?} 2[/tex]

Answers & Comments

onlyakem

Answer:

Is that correct? Or is that supposed to be

$\sqrt{2} \div \sqrt[3]{2}$

Radicals are basically exponents in fraction form. That's means:

$\sqrt{2} = {2}^{ \frac{1}{2} } \\ \sqrt[3]{2} = {2}^{ \frac{1}{3} }$

From there you basically have:

$\frac{ {2}^{ \frac{1}{2} } }{ {2}^{ \frac{1}{3} } }$

$\frac{\sqrt{2}}{\sqrt[3]{2}} \\ = \frac{\sqrt{2}}{\sqrt[3]{2}}\cdot \frac{\sqrt[3]{2^{2}}}{\sqrt[3]{2^{2}}} \\ = \frac{ \sqrt{2}\cdot \sqrt[3]{2^{2}} }{2} \\ = \frac{2^{ \frac{1}{2}+\frac{1}{3}}}{2} \\ =\frac{ 2^{ \frac{7}{6} } }{2} \\ = \frac{ \sqrt[6]{2^{7}} }{2} \\ = \frac{ 2\sqrt[6]{2} }{2}$

...

There you have it. Just continue solving it and you have your answer.

stacybudz thanks

stacybudz sana Makatulong yan

onlyakem Just one more step to do.

onlyakem The answer should be obvious

onlyakem What happens when the numerator and the denominator are the same?

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