3sqrt{22/3}div1/2sqrt{2/5}-1/8sqrt{15} eching

$$3 \sqrt{ 2 \frac{ 2 }{ 3 } } \div \frac{ 1 }{ 2 } \sqrt{ \frac{ 2 }{ 5 } } - \frac{ 1 }{ 8 } \sqrt{ 15 }$$

Baholash

$$\frac{59\sqrt{15}}{40}\approx 5,712650436$$

Yechim qadamlari

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

$$\frac{3\sqrt{\frac{6+2}{3}}}{\frac{1}{2}}\sqrt{\frac{2}{5}}-\frac{1}{8}\sqrt{15}$$

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

$$\frac{3\sqrt{\frac{8}{3}}}{\frac{1}{2}}\sqrt{\frac{2}{5}}-\frac{1}{8}\sqrt{15}$$

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

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

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.

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

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

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

\sqrt{3} kvadrati – 3.

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

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

$$\frac{3\times \frac{2\sqrt{6}}{3}}{\frac{1}{2}}\sqrt{\frac{2}{5}}-\frac{1}{8}\sqrt{15}$$

3 va 3 ni qisqartiring.

$$\frac{2\sqrt{6}}{\frac{1}{2}}\sqrt{\frac{2}{5}}-\frac{1}{8}\sqrt{15}$$

2\sqrt{6} ni \frac{1}{2} ga bo'lish 2\sqrt{6} ga k'paytirish \frac{1}{2} ga qaytarish.

$$2\sqrt{6}\times 2\sqrt{\frac{2}{5}}-\frac{1}{8}\sqrt{15}$$

4 hosil qilish uchun 2 va 2 ni ko'paytirish.

$$4\sqrt{6}\sqrt{\frac{2}{5}}-\frac{1}{8}\sqrt{15}$$

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

$$4\sqrt{6}\times \frac{\sqrt{2}}{\sqrt{5}}-\frac{1}{8}\sqrt{15}$$

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

$$4\sqrt{6}\times \frac{\sqrt{2}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}-\frac{1}{8}\sqrt{15}$$

\sqrt{5} kvadrati – 5.

$$4\sqrt{6}\times \frac{\sqrt{2}\sqrt{5}}{5}-\frac{1}{8}\sqrt{15}$$

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

$$4\sqrt{6}\times \frac{\sqrt{10}}{5}-\frac{1}{8}\sqrt{15}$$

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

$$\frac{4\sqrt{10}}{5}\sqrt{6}-\frac{1}{8}\sqrt{15}$$

\frac{4\sqrt{10}}{5}\sqrt{6} ni yagona kasrga aylantiring.

$$\frac{4\sqrt{10}\sqrt{6}}{5}-\frac{1}{8}\sqrt{15}$$

\sqrt{10} va \sqrt{6} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$\frac{4\sqrt{60}}{5}-\frac{1}{8}\sqrt{15}$$

Faktor: 60=2^{2}\times 15. \sqrt{2^{2}\times 15} koʻpaytmasining kvadrat ildizini \sqrt{2^{2}}\sqrt{15} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 2^{2} ning kvadrat ildizini chiqarish.

$$\frac{4\times 2\sqrt{15}}{5}-\frac{1}{8}\sqrt{15}$$

8 hosil qilish uchun 4 va 2 ni ko'paytirish.

$$\frac{8\sqrt{15}}{5}-\frac{1}{8}\sqrt{15}$$

\frac{59}{40}\sqrt{15} ni olish uchun \frac{8\sqrt{15}}{5} va -\frac{1}{8}\sqrt{15} ni birlashtirish.

$$\frac{59}{40}\sqrt{15}$$