sqrt{30}*3/2sqrt{22/3}div(-2sqrt{21/2}) eching

$$\sqrt { 30 } \times \frac { 3 } { 2 } \sqrt { 2 \frac { 2 } { 3 } } \div ( - 2 \sqrt { 2 \frac { 1 } { 2 } } )$$

Baholash

$$-3\sqrt{2}\approx -4,242640687$$

Yechim qadamlari

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

$$\frac{\sqrt{30}\times \frac{3}{2}\sqrt{\frac{6+2}{3}}}{-2\sqrt{\frac{2\times 2+1}{2}}}$$

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

$$\frac{\sqrt{30}\times \frac{3}{2}\sqrt{\frac{8}{3}}}{-2\sqrt{\frac{2\times 2+1}{2}}}$$

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

$$\frac{\sqrt{30}\times \frac{3}{2}\times \frac{\sqrt{8}}{\sqrt{3}}}{-2\sqrt{\frac{2\times 2+1}{2}}}$$

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.

$$\frac{\sqrt{30}\times \frac{3}{2}\times \frac{2\sqrt{2}}{\sqrt{3}}}{-2\sqrt{\frac{2\times 2+1}{2}}}$$

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

$$\frac{\sqrt{30}\times \frac{3}{2}\times \frac{2\sqrt{2}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}}{-2\sqrt{\frac{2\times 2+1}{2}}}$$

\sqrt{3} kvadrati – 3.

$$\frac{\sqrt{30}\times \frac{3}{2}\times \frac{2\sqrt{2}\sqrt{3}}{3}}{-2\sqrt{\frac{2\times 2+1}{2}}}$$

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

$$\frac{\sqrt{30}\times \frac{3}{2}\times \frac{2\sqrt{6}}{3}}{-2\sqrt{\frac{2\times 2+1}{2}}}$$

\sqrt{30}\times \frac{2\sqrt{6}}{3} ni yagona kasrga aylantiring.

$$\frac{\frac{\sqrt{30}\times 2\sqrt{6}}{3}\times \frac{3}{2}}{-2\sqrt{\frac{2\times 2+1}{2}}}$$

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

$$\frac{\frac{\sqrt{30}\times 2\sqrt{6}}{3}\times \frac{3}{2}}{-2\sqrt{\frac{4+1}{2}}}$$

5 olish uchun 4 va 1'ni qo'shing.

$$\frac{\frac{\sqrt{30}\times 2\sqrt{6}}{3}\times \frac{3}{2}}{-2\sqrt{\frac{5}{2}}}$$

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

$$\frac{\frac{\sqrt{30}\times 2\sqrt{6}}{3}\times \frac{3}{2}}{-2\times \frac{\sqrt{5}}{\sqrt{2}}}$$

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

$$\frac{\frac{\sqrt{30}\times 2\sqrt{6}}{3}\times \frac{3}{2}}{-2\times \frac{\sqrt{5}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}}$$

\sqrt{2} kvadrati – 2.

$$\frac{\frac{\sqrt{30}\times 2\sqrt{6}}{3}\times \frac{3}{2}}{-2\times \frac{\sqrt{5}\sqrt{2}}{2}}$$

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

$$\frac{\frac{\sqrt{30}\times 2\sqrt{6}}{3}\times \frac{3}{2}}{-2\times \frac{\sqrt{10}}{2}}$$

2 va 2 ni qisqartiring.

$$\frac{\frac{\sqrt{30}\times 2\sqrt{6}}{3}\times \frac{3}{2}}{-\sqrt{10}}$$

\frac{\frac{\sqrt{30}\times 2\sqrt{6}}{3}\times \frac{3}{2}}{-\sqrt{10}} maxrajini \sqrt{10} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{\frac{\sqrt{30}\times 2\sqrt{6}}{3}\times \frac{3}{2}\sqrt{10}}{-\left(\sqrt{10}\right)^{2}}$$

\sqrt{10} kvadrati – 10.

$$\frac{\frac{\sqrt{30}\times 2\sqrt{6}}{3}\times \frac{3}{2}\sqrt{10}}{-10}$$

Faktor: 30=6\times 5. \sqrt{6\times 5} koʻpaytmasining kvadrat ildizini \sqrt{6}\sqrt{5} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing.

$$\frac{\frac{\sqrt{6}\sqrt{5}\times 2\sqrt{6}}{3}\times \frac{3}{2}\sqrt{10}}{-10}$$

6 hosil qilish uchun \sqrt{6} va \sqrt{6} ni ko'paytirish.

$$\frac{\frac{6\times 2\sqrt{5}}{3}\times \frac{3}{2}\sqrt{10}}{-10}$$

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

$$\frac{\frac{12\sqrt{5}}{3}\times \frac{3}{2}\sqrt{10}}{-10}$$

4\sqrt{5} ni olish uchun 12\sqrt{5} ni 3 ga bo‘ling.

$$\frac{4\sqrt{5}\times \frac{3}{2}\sqrt{10}}{-10}$$

4\times \frac{3}{2} ni yagona kasrga aylantiring.

$$\frac{\frac{4\times 3}{2}\sqrt{5}\sqrt{10}}{-10}$$

12 hosil qilish uchun 4 va 3 ni ko'paytirish.

$$\frac{\frac{12}{2}\sqrt{5}\sqrt{10}}{-10}$$

6 ni olish uchun 12 ni 2 ga bo‘ling.

$$\frac{6\sqrt{5}\sqrt{10}}{-10}$$

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

$$\frac{6\sqrt{5}\sqrt{5}\sqrt{2}}{-10}$$

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

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

30 hosil qilish uchun 6 va 5 ni ko'paytirish.

$$\frac{30\sqrt{2}}{-10}$$

-3\sqrt{2} ni olish uchun 30\sqrt{2} ni -10 ga bo‘ling.

$$-3\sqrt{2}$$