frac{6/3sqrt{17+27}}{8} eching

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

Baholash

$$\frac{9-\sqrt{17}}{256}\approx 0,019050369$$

Yechim qadamlari

\frac{\frac{6}{3\sqrt{17}+27}}{8} ni yagona kasrga aylantiring.

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

3\sqrt{17}+27 ga 8 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

\frac{6}{24\sqrt{17}+216} maxrajini 24\sqrt{17}-216 orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

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

Hisoblang: \left(24\sqrt{17}+216\right)\left(24\sqrt{17}-216\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

\left(24\sqrt{17}\right)^{2} ni kengaytirish.

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

2 daraja ko‘rsatkichini 24 ga hisoblang va 576 ni qiymatni oling.

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

\sqrt{17} kvadrati – 17.

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

9792 hosil qilish uchun 576 va 17 ni ko'paytirish.

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

2 daraja ko‘rsatkichini 216 ga hisoblang va 46656 ni qiymatni oling.

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

-36864 olish uchun 9792 dan 46656 ni ayirish.

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

-\frac{1}{6144}\left(24\sqrt{17}-216\right) ni olish uchun 6\left(24\sqrt{17}-216\right) ni -36864 ga bo‘ling.

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

-\frac{1}{6144} ga 24\sqrt{17}-216 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

-\frac{1}{6144}\times 24 ni yagona kasrga aylantiring.

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

\frac{-24}{6144} ulushini 24 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

-\frac{1}{6144}\left(-216\right) ni yagona kasrga aylantiring.

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

216 hosil qilish uchun -1 va -216 ni ko'paytirish.

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

\frac{216}{6144} ulushini 24 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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