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Rationalisation

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

Note by Swapnil Das
2 years, 2 months ago

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Let 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 · 2 years, 2 months ago

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@Santanu Banerjee Can you explain what is the motivation behind "Multiply with \( x^2 - x + 1 \)?"

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 · 2 years, 2 months ago

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@Calvin Lin Can you please explain the answer to your question? Rama Devi · 1 year, 12 months ago

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@Rama Devi Hello, please see the problem " Inspired by Swapnil Das". Swapnil Das · 1 year, 12 months ago

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@Swapnil Das I couldn't understand these solutions that are posted.Can you tell an easy method? Please Rama Devi · 1 year, 12 months ago

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@Rama Devi Please give your response soon. Rama Devi · 1 year, 12 months ago

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@Santanu Banerjee Doubt again. Why should we multiply the given expression? Swapnil Das · 2 years, 2 months ago

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@Swapnil Das he used this identity \[\displaystyle{\left( { x }^{ 3 }+1 \right) =\left( x+1 \right) \left( { x }^{ 2 }-x+1 \right) }\] Vighnesh Raut · 2 years, 2 months ago

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@Santanu Banerjee Thank You Swapnil Das · 2 years, 2 months ago

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