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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, 7 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, 7 months ago

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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, 7 months ago

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Can you please explain the answer to your question?

Rama Devi - 2 years, 4 months ago

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@Rama Devi Hello, please see the problem " Inspired by Swapnil Das".

Swapnil Das - 2 years, 4 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 - 2 years, 4 months ago

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@Rama Devi Please give your response soon.

Rama Devi - 2 years, 4 months ago

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Doubt again. Why should we multiply the given expression?

Swapnil Das - 2 years, 7 months ago

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

Vighnesh Raut - 2 years, 7 months ago

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Thank You

Swapnil Das - 2 years, 7 months ago

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