sqrt{13/5}div22sqrt{1/5}*sqrt{63}= eching

$$\sqrt { 1 \frac { 3 } { 5 } } \div 22 \sqrt { \frac { 1 } { 5 } } \times \sqrt { 63 } =$$

Baholash

$$\frac{3\sqrt{14}}{55}\approx 0,204090403$$

Yechim qadamlari

5 hosil qilish uchun 1 va 5 ni ko'paytirish.

$$\frac{\sqrt{\frac{5+3}{5}}}{22}\sqrt{\frac{1}{5}}\sqrt{63}$$

8 olish uchun 5 va 3'ni qo'shing.

$$\frac{\sqrt{\frac{8}{5}}}{22}\sqrt{\frac{1}{5}}\sqrt{63}$$

\sqrt{\frac{8}{5}} boʻlinmasining kvadrat ildizini \frac{\sqrt{8}}{\sqrt{5}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

$$\frac{\frac{\sqrt{8}}{\sqrt{5}}}{22}\sqrt{\frac{1}{5}}\sqrt{63}$$

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.

$$\frac{\frac{2\sqrt{2}}{\sqrt{5}}}{22}\sqrt{\frac{1}{5}}\sqrt{63}$$

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

$$\frac{\frac{2\sqrt{2}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}}{22}\sqrt{\frac{1}{5}}\sqrt{63}$$

\sqrt{5} kvadrati – 5.

$$\frac{\frac{2\sqrt{2}\sqrt{5}}{5}}{22}\sqrt{\frac{1}{5}}\sqrt{63}$$

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

$$\frac{\frac{2\sqrt{10}}{5}}{22}\sqrt{\frac{1}{5}}\sqrt{63}$$

\frac{\frac{2\sqrt{10}}{5}}{22} ni yagona kasrga aylantiring.

$$\frac{2\sqrt{10}}{5\times 22}\sqrt{\frac{1}{5}}\sqrt{63}$$

Surat va maxrajdagi ikkala 2 ni qisqartiring.

$$\frac{\sqrt{10}}{5\times 11}\sqrt{\frac{1}{5}}\sqrt{63}$$

55 hosil qilish uchun 5 va 11 ni ko'paytirish.

$$\frac{\sqrt{10}}{55}\sqrt{\frac{1}{5}}\sqrt{63}$$

\sqrt{\frac{1}{5}} boʻlinmasining kvadrat ildizini \frac{\sqrt{1}}{\sqrt{5}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

$$\frac{\sqrt{10}}{55}\times \frac{\sqrt{1}}{\sqrt{5}}\sqrt{63}$$

1 ning kvadrat ildizini hisoblab, 1 natijaga ega bo‘ling.

$$\frac{\sqrt{10}}{55}\times \frac{1}{\sqrt{5}}\sqrt{63}$$

\frac{1}{\sqrt{5}} maxrajini \sqrt{5} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{\sqrt{10}}{55}\times \frac{\sqrt{5}}{\left(\sqrt{5}\right)^{2}}\sqrt{63}$$

\sqrt{5} kvadrati – 5.

$$\frac{\sqrt{10}}{55}\times \frac{\sqrt{5}}{5}\sqrt{63}$$

Faktor: 63=3^{2}\times 7. \sqrt{3^{2}\times 7} koʻpaytmasining kvadrat ildizini \sqrt{3^{2}}\sqrt{7} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 3^{2} ning kvadrat ildizini chiqarish.

$$\frac{\sqrt{10}}{55}\times \frac{\sqrt{5}}{5}\times 3\sqrt{7}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{\sqrt{10}}{55} ni \frac{\sqrt{5}}{5} ga ko‘paytiring.

$$\frac{\sqrt{10}\sqrt{5}}{55\times 5}\times 3\sqrt{7}$$

\frac{\sqrt{10}\sqrt{5}}{55\times 5}\times 3 ni yagona kasrga aylantiring.

$$\frac{\sqrt{10}\sqrt{5}\times 3}{55\times 5}\sqrt{7}$$

\frac{\sqrt{10}\sqrt{5}\times 3}{55\times 5}\sqrt{7} ni yagona kasrga aylantiring.

$$\frac{\sqrt{10}\sqrt{5}\times 3\sqrt{7}}{55\times 5}$$

Faktor: 10=5\times 2. \sqrt{5\times 2} koʻpaytmasining kvadrat ildizini \sqrt{5}\sqrt{2} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing.

$$\frac{\sqrt{5}\sqrt{2}\sqrt{5}\times 3\sqrt{7}}{55\times 5}$$

5 hosil qilish uchun \sqrt{5} va \sqrt{5} ni ko'paytirish.

$$\frac{5\sqrt{2}\times 3\sqrt{7}}{55\times 5}$$

15 hosil qilish uchun 5 va 3 ni ko'paytirish.

$$\frac{15\sqrt{2}\sqrt{7}}{55\times 5}$$

\sqrt{2} va \sqrt{7} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$\frac{15\sqrt{14}}{55\times 5}$$

275 hosil qilish uchun 55 va 5 ni ko'paytirish.

$$\frac{15\sqrt{14}}{275}$$

\frac{3}{55}\sqrt{14} ni olish uchun 15\sqrt{14} ni 275 ga bo‘ling.

$$\frac{3}{55}\sqrt{14}$$