3sqrt{22/3}+1/2sqrt{2/5}*(-1/8sqrt{15}) eching

$$3 \sqrt { 2 \frac { 2 } { 3 } } + \frac { 1 } { 2 } \sqrt { \frac { 2 } { 5 } } \times ( - \frac { 1 } { 8 } \sqrt { 15 } )$$

Baholash

$$\frac{31\sqrt{6}}{16}\approx 4,745886377$$

Qisqa yechim qadamlari

6 hosil qilish uchun 2 va 3 ni ko'paytirish.

$$3\sqrt{\frac{6+2}{3}}+\frac{1}{2}\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

8 olish uchun 6 va 2'ni qo'shing.

$$3\sqrt{\frac{8}{3}}+\frac{1}{2}\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

\sqrt{\frac{8}{3}} boʻlinmasining kvadrat ildizini \frac{\sqrt{8}}{\sqrt{3}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

$$3\times \frac{\sqrt{8}}{\sqrt{3}}+\frac{1}{2}\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

Faktor: 8=2^{2}\times 2. \sqrt{2^{2}\times 2} koʻpaytmasining kvadrat ildizini \sqrt{2^{2}}\sqrt{2} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 2^{2} ning kvadrat ildizini chiqarish.

$$3\times \frac{2\sqrt{2}}{\sqrt{3}}+\frac{1}{2}\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

\frac{2\sqrt{2}}{\sqrt{3}} maxrajini \sqrt{3} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$3\times \frac{2\sqrt{2}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}+\frac{1}{2}\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

\sqrt{3} kvadrati – 3.

$$3\times \frac{2\sqrt{2}\sqrt{3}}{3}+\frac{1}{2}\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

\sqrt{2} va \sqrt{3} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$3\times \frac{2\sqrt{6}}{3}+\frac{1}{2}\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

3 va 3 ni qisqartiring.

$$2\sqrt{6}+\frac{1}{2}\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

\sqrt{\frac{2}{5}} boʻlinmasining kvadrat ildizini \frac{\sqrt{2}}{\sqrt{5}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

$$2\sqrt{6}+\frac{1}{2}\times \frac{\sqrt{2}}{\sqrt{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

\frac{\sqrt{2}}{\sqrt{5}} maxrajini \sqrt{5} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$2\sqrt{6}+\frac{1}{2}\times \frac{\sqrt{2}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}\left(-\frac{1}{8}\right)\sqrt{15}$$

\sqrt{5} kvadrati – 5.

$$2\sqrt{6}+\frac{1}{2}\times \frac{\sqrt{2}\sqrt{5}}{5}\left(-\frac{1}{8}\right)\sqrt{15}$$

\sqrt{2} va \sqrt{5} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$2\sqrt{6}+\frac{1}{2}\times \frac{\sqrt{10}}{5}\left(-\frac{1}{8}\right)\sqrt{15}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{1}{2} ni -\frac{1}{8} ga ko‘paytiring.

$$2\sqrt{6}+\frac{1\left(-1\right)}{2\times 8}\times \frac{\sqrt{10}}{5}\sqrt{15}$$

\frac{1\left(-1\right)}{2\times 8} kasridagi ko‘paytirishlarni bajaring.

$$2\sqrt{6}+\frac{-1}{16}\times \frac{\sqrt{10}}{5}\sqrt{15}$$

\frac{-1}{16} kasri manfiy belgini olib tashlash bilan -\frac{1}{16} sifatida qayta yozilishi mumkin.

$$2\sqrt{6}-\frac{1}{16}\times \frac{\sqrt{10}}{5}\sqrt{15}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali -\frac{1}{16} ni \frac{\sqrt{10}}{5} ga ko‘paytiring.

$$2\sqrt{6}+\frac{-\sqrt{10}}{16\times 5}\sqrt{15}$$

\frac{-\sqrt{10}}{16\times 5}\sqrt{15} ni yagona kasrga aylantiring.

$$2\sqrt{6}+\frac{-\sqrt{10}\sqrt{15}}{16\times 5}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 2\sqrt{6} ni \frac{16\times 5}{16\times 5} marotabaga ko'paytirish.

$$\frac{2\sqrt{6}\times 16\times 5}{16\times 5}+\frac{-\sqrt{10}\sqrt{15}}{16\times 5}$$

\frac{2\sqrt{6}\times 16\times 5}{16\times 5} va \frac{-\sqrt{10}\sqrt{15}}{16\times 5} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{2\sqrt{6}\times 16\times 5-\sqrt{10}\sqrt{15}}{16\times 5}$$

2\sqrt{6}\times 16\times 5-\sqrt{10}\sqrt{15} ichidagi ko‘paytirishlarni bajaring.

$$\frac{160\sqrt{6}-5\sqrt{6}}{16\times 5}$$

160\sqrt{6}-5\sqrt{6} hisob-kitobini qiling.

$$\frac{155\sqrt{6}}{16\times 5}$$

Surat va maxrajdagi ikkala 5 ni qisqartiring.

$$\frac{31\sqrt{6}}{16}$$