Réitigh frac{6/3sqrt{17+27}}{8}

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

Luacháil

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

Céimeanna Réitigh

Scríobh \frac{\frac{6}{3\sqrt{17}+27}}{8} mar chodán aonair.

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

Úsáid an t-airí dáileach chun 3\sqrt{17}+27 a mhéadú faoi 8.

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

Iolraigh an t-uimhreoir agus an t-ainmneoir faoi 24\sqrt{17}-216 chun ainmneoir \frac{6}{24\sqrt{17}+216} a thiontú in uimhir chóimheasta.

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

Mar shampla \left(24\sqrt{17}+216\right)\left(24\sqrt{17}-216\right). Is féidir iolrúchán a athrú ó bhonn go dtí difríocht na gcearnóg ag úsáid na rialach seo: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Fairsingigh \left(24\sqrt{17}\right)^{2}

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

Ríomh cumhacht 24 de 2 agus faigh 576.

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

Is é 17 uimhir chearnach \sqrt{17}.

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

Méadaigh 576 agus 17 chun 9792 a fháil.

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

Ríomh cumhacht 216 de 2 agus faigh 46656.

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

Dealaigh 46656 ó 9792 chun -36864 a fháil.

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

Roinn 6\left(24\sqrt{17}-216\right) faoi -36864 chun -\frac{1}{6144}\left(24\sqrt{17}-216\right) a fháil.

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

Úsáid an t-airí dáileach chun -\frac{1}{6144} a mhéadú faoi 24\sqrt{17}-216.

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

Scríobh -\frac{1}{6144}\times 24 mar chodán aonair.

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

Laghdaigh an codán \frac{-24}{6144} chuig na téarmaí is ísle trí 24 a bhaint agus a chealú.

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

Scríobh -\frac{1}{6144}\left(-216\right) mar chodán aonair.

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

Méadaigh -1 agus -216 chun 216 a fháil.

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

Laghdaigh an codán \frac{216}{6144} chuig na téarmaí is ísle trí 24 a bhaint agus a chealú.

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