展开 (11(3sqrt(11)+3sqrt(3)-3-sqrt(33)))/(12)

解答

展开

\frac{11 ( 3 11 + 3 3 - 3 - 33 )}{12}

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

十进制

5.86800 \dots

求解步骤

\frac{11 ( 3 11 + 3 3 - 3 - 33 )}{12}

乘开

11 (311 + 33 - 3 - 33) : 3311 + 333 - 33 - 1133

= \frac{33 11 + 33 3 - 33 - 11 33}{12}

使用分式法则:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{33 11 + 33 3 - 33 - 11 33}{12} = \frac{33 11}{12} + \frac{33 3}{12} - \frac{33}{12} - \frac{11 33}{12}

= \frac{33 11}{12} + \frac{33 3}{12} - \frac{33}{12} - \frac{11 33}{12}

\frac{33 11}{12} = \frac{11 11}{4}

\frac{33 3}{12} = \frac{11 3}{4}

\frac{33}{12} = \frac{11}{4}

\frac{11 33}{12} = \frac{11 11}{4 3}

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

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