Whakaoti i te frac{6/3sqrt{17+27}}{8}

$$\frac { \frac { 6 } { 3 \sqrt { 17 } + 27 } } { 8 }$$

Aromātai

$$\frac{9-\sqrt{17}}{256}\approx 0.019050369$$

Ngā Upane Otinga

Tuhia te \frac{\frac{6}{3\sqrt{17}+27}}{8} hei hautanga kotahi.

$$\frac{6}{\left(3\sqrt{17}+27\right)\times 8}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3\sqrt{17}+27 ki te 8.

$$\frac{6}{24\sqrt{17}+216}$$

Whakangāwaritia te tauraro o \frac{6}{24\sqrt{17}+216} mā te whakarea i te taurunga me te tauraro ki te 24\sqrt{17}-216.

$$\frac{6\left(24\sqrt{17}-216\right)}{\left(24\sqrt{17}+216\right)\left(24\sqrt{17}-216\right)}$$

Whakaarohia te \left(24\sqrt{17}+216\right)\left(24\sqrt{17}-216\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{6\left(24\sqrt{17}-216\right)}{\left(24\sqrt{17}\right)^{2}-216^{2}}$$

Whakarohaina te \left(24\sqrt{17}\right)^{2}.

$$\frac{6\left(24\sqrt{17}-216\right)}{24^{2}\left(\sqrt{17}\right)^{2}-216^{2}}$$

Tātaihia te 24 mā te pū o 2, kia riro ko 576.

$$\frac{6\left(24\sqrt{17}-216\right)}{576\left(\sqrt{17}\right)^{2}-216^{2}}$$

Ko te pūrua o \sqrt{17} ko 17.

$$\frac{6\left(24\sqrt{17}-216\right)}{576\times 17-216^{2}}$$

Whakareatia te 576 ki te 17, ka 9792.

$$\frac{6\left(24\sqrt{17}-216\right)}{9792-216^{2}}$$

Tātaihia te 216 mā te pū o 2, kia riro ko 46656.

$$\frac{6\left(24\sqrt{17}-216\right)}{9792-46656}$$

Tangohia te 46656 i te 9792, ka -36864.

$$\frac{6\left(24\sqrt{17}-216\right)}{-36864}$$

Whakawehea te 6\left(24\sqrt{17}-216\right) ki te -36864, kia riro ko -\frac{1}{6144}\left(24\sqrt{17}-216\right).

$$-\frac{1}{6144}\left(24\sqrt{17}-216\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -\frac{1}{6144} ki te 24\sqrt{17}-216.

$$-\frac{1}{6144}\times 24\sqrt{17}-\frac{1}{6144}\left(-216\right)$$

Tuhia te -\frac{1}{6144}\times 24 hei hautanga kotahi.

$$\frac{-24}{6144}\sqrt{17}-\frac{1}{6144}\left(-216\right)$$

Whakahekea te hautanga \frac{-24}{6144} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 24.

$$-\frac{1}{256}\sqrt{17}-\frac{1}{6144}\left(-216\right)$$

Tuhia te -\frac{1}{6144}\left(-216\right) hei hautanga kotahi.

$$-\frac{1}{256}\sqrt{17}+\frac{-\left(-216\right)}{6144}$$

Whakareatia te -1 ki te -216, ka 216.

$$-\frac{1}{256}\sqrt{17}+\frac{216}{6144}$$

Whakahekea te hautanga \frac{216}{6144} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 24.

$$-\frac{1}{256}\sqrt{17}+\frac{9}{256}$$