Rationalisation

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

#MathProblem

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

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 - 6 years, 2 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 $\frac{1}{ \sqrt{2} + \sqrt[3] { 3} }$ ?

Calvin Lin Staff - 6 years, 2 months ago

Can you please explain the answer to your question?

Rama Devi - 6 years ago

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

Swapnil Das - 6 years ago

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

Rama Devi - 6 years ago

@Rama Devi – Please give your response soon.

Rama Devi - 6 years ago

Thank You

Swapnil Das - 6 years, 2 months ago

Doubt again. Why should we multiply the given expression?

Swapnil Das - 6 years, 2 months ago

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

Vighnesh Raut - 6 years, 2 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$