# Rationalisation

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

Note by Swapnil Das
3 years, 6 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.

- 3 years, 6 months ago

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 $$\frac{1}{ \sqrt{2} + \sqrt[3] { 3} }$$?

Staff - 3 years, 6 months ago

- 3 years, 3 months ago

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

- 3 years, 3 months ago

I couldn't understand these solutions that are posted.Can you tell an easy method? Please

- 3 years, 3 months ago

- 3 years, 3 months ago

Doubt again. Why should we multiply the given expression?

- 3 years, 6 months ago

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

- 3 years, 6 months ago

Thank You

- 3 years, 6 months ago