I have a doubt. How do you rationalize the following expression? \(\frac{1}{\sqrt[3]{2} + 1}\)

I have a doubt. How do you rationalize the following expression? \(\frac{1}{\sqrt[3]{2} + 1}\)

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TopNewestLet cube root of 2 be x.

Then multiply above and below with (x^2 - x + 1).

You get the denominator as (x^3 + 1) = 3 a rational number. – Santanu Banerjee · 1 year, 7 months ago

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For another expression, how do we determine what to do?

E.g. how do you rationalize \( \frac{1}{ \sqrt{2} + \sqrt[3] { 3} } \)? – Calvin Lin Staff · 1 year, 7 months ago

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– Rama Devi · 1 year, 4 months ago

Can you please explain the answer to your question?Log in to reply

– Swapnil Das · 1 year, 4 months ago

Hello, please see the problem " Inspired by Swapnil Das".Log in to reply

– Rama Devi · 1 year, 4 months ago

I couldn't understand these solutions that are posted.Can you tell an easy method? PleaseLog in to reply

– Rama Devi · 1 year, 4 months ago

Please give your response soon.Log in to reply

– Swapnil Das · 1 year, 7 months ago

Doubt again. Why should we multiply the given expression?Log in to reply

– Vighnesh Raut · 1 year, 7 months ago

he used this identity \[\displaystyle{\left( { x }^{ 3 }+1 \right) =\left( x+1 \right) \left( { x }^{ 2 }-x+1 \right) }\]Log in to reply

– Swapnil Das · 1 year, 7 months ago

Thank YouLog in to reply