sqrt{16/15:7/8-13/15:13/10+frac{1}{3}*frac{5}{3}}= eching

$$\sqrt { \frac { 16 } { 15 } : \frac { 7 } { 8 } - \frac { 13 } { 15 } : \frac { 13 } { 10 } + \frac { 1 } { 3 } \times \frac { 5 } { 3 } } =$$

Baholash

$$\frac{\sqrt{12215}}{105}\approx 1,05258563$$

Yechim qadamlari

\frac{16}{15} ni \frac{7}{8} ga bo'lish \frac{16}{15} ga k'paytirish \frac{7}{8} ga qaytarish.

$$\sqrt{\frac{16}{15}\times \frac{8}{7}-\frac{\frac{13}{15}}{\frac{13}{10}}+\frac{1}{3}\times \frac{5}{3}}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{16}{15} ni \frac{8}{7} ga ko‘paytiring.

$$\sqrt{\frac{16\times 8}{15\times 7}-\frac{\frac{13}{15}}{\frac{13}{10}}+\frac{1}{3}\times \frac{5}{3}}$$

\frac{16\times 8}{15\times 7} kasridagi ko‘paytirishlarni bajaring.

$$\sqrt{\frac{128}{105}-\frac{\frac{13}{15}}{\frac{13}{10}}+\frac{1}{3}\times \frac{5}{3}}$$

\frac{13}{15} ni \frac{13}{10} ga bo'lish \frac{13}{15} ga k'paytirish \frac{13}{10} ga qaytarish.

$$\sqrt{\frac{128}{105}-\frac{13}{15}\times \frac{10}{13}+\frac{1}{3}\times \frac{5}{3}}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{13}{15} ni \frac{10}{13} ga ko‘paytiring.

$$\sqrt{\frac{128}{105}-\frac{13\times 10}{15\times 13}+\frac{1}{3}\times \frac{5}{3}}$$

Surat va maxrajdagi ikkala 13 ni qisqartiring.

$$\sqrt{\frac{128}{105}-\frac{10}{15}+\frac{1}{3}\times \frac{5}{3}}$$

\frac{10}{15} ulushini 5 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\sqrt{\frac{128}{105}-\frac{2}{3}+\frac{1}{3}\times \frac{5}{3}}$$

105 va 3 ning eng kichik umumiy karralisi 105 ga teng. \frac{128}{105} va \frac{2}{3} ni 105 maxraj bilan kasrlarga aylantirib oling.

$$\sqrt{\frac{128}{105}-\frac{70}{105}+\frac{1}{3}\times \frac{5}{3}}$$

\frac{128}{105} va \frac{70}{105} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\sqrt{\frac{128-70}{105}+\frac{1}{3}\times \frac{5}{3}}$$

58 olish uchun 128 dan 70 ni ayirish.

$$\sqrt{\frac{58}{105}+\frac{1}{3}\times \frac{5}{3}}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{1}{3} ni \frac{5}{3} ga ko‘paytiring.

$$\sqrt{\frac{58}{105}+\frac{1\times 5}{3\times 3}}$$

\frac{1\times 5}{3\times 3} kasridagi ko‘paytirishlarni bajaring.

$$\sqrt{\frac{58}{105}+\frac{5}{9}}$$

105 va 9 ning eng kichik umumiy karralisi 315 ga teng. \frac{58}{105} va \frac{5}{9} ni 315 maxraj bilan kasrlarga aylantirib oling.

$$\sqrt{\frac{174}{315}+\frac{175}{315}}$$

\frac{174}{315} va \frac{175}{315} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\sqrt{\frac{174+175}{315}}$$

349 olish uchun 174 va 175'ni qo'shing.

$$\sqrt{\frac{349}{315}}$$

\sqrt{\frac{349}{315}} boʻlinmasining kvadrat ildizini \frac{\sqrt{349}}{\sqrt{315}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

$$\frac{\sqrt{349}}{\sqrt{315}}$$

Faktor: 315=3^{2}\times 35. \sqrt{3^{2}\times 35} koʻpaytmasining kvadrat ildizini \sqrt{3^{2}}\sqrt{35} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 3^{2} ning kvadrat ildizini chiqarish.

$$\frac{\sqrt{349}}{3\sqrt{35}}$$

\frac{\sqrt{349}}{3\sqrt{35}} maxrajini \sqrt{35} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{\sqrt{349}\sqrt{35}}{3\left(\sqrt{35}\right)^{2}}$$

\sqrt{35} kvadrati – 35.

$$\frac{\sqrt{349}\sqrt{35}}{3\times 35}$$

\sqrt{349} va \sqrt{35} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$\frac{\sqrt{12215}}{3\times 35}$$

105 hosil qilish uchun 3 va 35 ni ko'paytirish.

$$\frac{\sqrt{12215}}{105}$$