What is (sqrt(3))/(4+sqrt(19)) ?

The solution to (sqrt(3))/(4+sqrt(19)) is -(4sqrt(3)-sqrt(57))/3

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simplify (sqrt(3))/(4+sqrt(19))

simplify

\frac{3}{4 + 19}

- \frac{4 3 - 57}{3}

Decimal Notation

0.20721 \dots

Solution steps

\frac{3}{4 + 19}

Multiply by the conjugate

\frac{4 - 19}{4 - 19}

= \frac{3 ( 4 - 19 )}{( 4 + 19 ) ( 4 - 19 )}

Expand

3 (4 - 19) : 43 - 57

Expand

(4 + 19) (4 - 19) : - 3

= \frac{4 3 - 57}{- 3}

Apply the fraction rule:

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

= - \frac{4 3 - 57}{3}

ln (- \frac{7}{2}) + ln (2 (- \frac{7}{2}) + 5) = ln (7)

16 - b^{4}

x^{2} + 6 x + 25 = 0

4 x - 9 = - 6 x + 11

8^{2} + 9

What is (sqrt(3))/(4+sqrt(19)) ?
The solution to (sqrt(3))/(4+sqrt(19)) is -(4sqrt(3)-sqrt(57))/3