approximation

**thereddevils** · September 5th 2009, 02:19 AM

Write down the first three terms in the binomial expansion of $\sqrt[4]{1+\frac{x}{81}}$
Here i got

$1+\frac{x}{324}-\frac{x^2}{69984}$

Then deduce that $\sqrt[4]{80}=2.9907$ .. not sure with this part

That should be the approximation sign , i am not sure how to do it with latex .

**mr fantastic** · September 5th 2009, 03:03 AM

Originally Posted by thereddevils

Write down the first three terms in the binomial expansion of $\sqrt[4]{1+\frac{x}{81}}$
Here i got

$1+\frac{x}{324}-\frac{x^2}{69984}$

Then deduce that $\sqrt[4]{80}=2.9907$ .. not sure with this part

That should be the approximation sign , i am not sure how to do it with latex .

Note that $\sqrt[4]{1+\frac{x}{81}} = \sqrt[4]{\frac{81+x}{81}} = \frac{1}{3} \sqrt[4]{81+x}$ so substitute $x = -1$ into the approximate expansion of $\sqrt[4]{1+\frac{x}{81}}$ and then re-arrange to get the approximate value of $\sqrt[4]{80}$ .

**thereddevils** · September 5th 2009, 04:46 AM

Originally Posted by mr fantastic

Note that $\sqrt[4]{1+\frac{x}{81}} = \sqrt[4]{\frac{81+x}{81}} = \frac{1}{3} \sqrt[4]{81+x}$ so substitute $x = -1$ into the approximate expansion of $\sqrt[4]{1+\frac{x}{81}}$ and then re-arrange to get the approximate value of $\sqrt[4]{80}$ .

THank you .

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