What is 2/(sqrt(13)+\sqrt{11)} ?

The solution to 2/(sqrt(13)+\sqrt{11)} is sqrt(13)-sqrt(11)

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simplify 2/(sqrt(13)+\sqrt{11)}

simplify

\frac{2}{13 + 11}

13 - 11

Decimal Notation

0.28892 \dots

Solution steps

\frac{2}{13 + 11}

Multiply by the conjugate

\frac{13 - 11}{13 - 11}

= \frac{2 ( 13 - 11 )}{( 13 + 11 ) ( 13 - 11 )}

Expand

2 (13 - 11) : 213 - 211

Expand

(13 + 11) (13 - 11) : 2

= \frac{2 13 - 2 11}{2}

Factor out common term

2

= \frac{2 ( 13 - 11 )}{2}

Cancel the common factor:

2

= 13 - 11

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- 3 - 4

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What is 2/(sqrt(13)+\sqrt{11)} ?
The solution to 2/(sqrt(13)+\sqrt{11)} is sqrt(13)-sqrt(11)