How do you rationalize the denominator and simplify $1/(1-8sqrt2)$ ?

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Answer 1 · 2018-03-25T03:10:45

I believe this should be simplified as $(-(8sqrt2+1))/127$ .

To rationalize the denominator, you must multiply the term that has the $sqrt$ by itself, to move it to the numerator. So:

$=>$ $1/(1-8*sqrt2)*8sqrt2$

This will give:

$=>$ $(8sqrt2+1)/(1-(8sqrt2)^2$

$(8sqrt2)^2=64*2=128$

$=>$ $(8sqrt2+1)/(1-128)$

$=>$ $(8sqrt2+1)/-127$

The negative cam also be moved to the top, for:

$=>$ $(-(8sqrt2+1))/127$

Answer 2 · 2018-03-25T03:14:30

$(-1-8sqrt2)/127$

Multiply the numerator and the denominator by the surd (to undo the surd) and the negative of the extra value.

$1/(1-8sqrt2$ x $(-1+8sqrt2)/(-1+8sqrt2$

$(1(1+8sqrt2))/((1-8sqrt2)(1+8sqrt2)$

Expand brackets. Use the FOIL rule for the denominator.

$(1+8sqrt2)/-127$

You could simplify further by taking the negative of the denominator and apply it to the numerator.

$(-1-8sqrt2)/127$

How do you rationalize the denominator and simplify 1/(1-8sqrt2)1/(1-8sqrt2)?