What is 1/(1+sqrt(11)) ?

The solution to 1/(1+sqrt(11)) is (sqrt(11)-1)/(10)

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simplify 1/(1+sqrt(11))

simplify

\frac{1}{1 + 11}

\frac{11 - 1}{10}

Decimal Notation

0.23166 \dots

Solution steps

\frac{1}{1 + 11}

Multiply by the conjugate

\frac{1 - 11}{1 - 11}

= \frac{1 \cdot ( 1 - 11 )}{( 1 + 11 ) ( 1 - 11 )}

1 \cdot (1 - 11) = 1 - 11

(1 + 11) (1 - 11) = - 10

= \frac{1 - 11}{- 10}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

1 - 11 = - (11 - 1)

= \frac{11 - 1}{10}

\frac{7 π}{6} + 2 πn

64 - 25 v^{2}

20 > 5 x

2 a^{4} + 24 a^{2} + 64

- (\frac{3}{4})^{3}