What is 1/(3*sqrt(3)+4) ?

The solution to 1/(3*sqrt(3)+4) is (3sqrt(3)-4)/(11)

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simplify 1/(3*sqrt(3)+4)

simplify

\frac{1}{3 \cdot 3 + 4}

\frac{3 3 - 4}{11}

Decimal Notation

0.10874 \dots

Solution steps

\frac{1}{3 3 + 4}

Multiply by the conjugate

\frac{3 3 - 4}{3 3 - 4}

= \frac{1 \cdot ( 3 3 - 4 )}{( 3 3 + 4 ) ( 3 3 - 4 )}

1 \cdot (33 - 4) = 33 - 4

(33 + 4) (33 - 4) = 11

= \frac{3 3 - 4}{11}

\frac{81}{36}

\frac{3}{16}

\frac{20}{400}

x^{3} - 5 x^{2} + 12 x - 8

5 (0.1 x - 0.2) + 10 x