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

Mar 25, 2018

I believe this should be simplified as $\frac{- \left(8 \sqrt{2} + 1\right)}{127}$.

#### Explanation:

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

$\implies$$\frac{1}{1 - 8 \cdot \sqrt{2}} \cdot 8 \sqrt{2}$

This will give:

$\implies$(8sqrt2+1)/(1-(8sqrt2)^2

${\left(8 \sqrt{2}\right)}^{2} = 64 \cdot 2 = 128$

$\implies$$\frac{8 \sqrt{2} + 1}{1 - 128}$

$\implies$$\frac{8 \sqrt{2} + 1}{-} 127$

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

$\implies$$\frac{- \left(8 \sqrt{2} + 1\right)}{127}$

Mar 25, 2018

$\frac{- 1 - 8 \sqrt{2}}{127}$

#### Explanation:

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.

$\frac{1 + 8 \sqrt{2}}{-} 127$

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

$\frac{- 1 - 8 \sqrt{2}}{127}$