3sqrt{22/3}div2sqrt{2/5}*(-1/8sqrt{15}) eching

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

Baholash

$$-\frac{3}{4}=-0,75$$

Yechim qadamlari

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

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

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

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

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

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

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.

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

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

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

\sqrt{3} kvadrati – 3.

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

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

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

3 va 3 ni qisqartiring.

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

2 va 2 ni qisqartiring.

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

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

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

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

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

\sqrt{5} kvadrati – 5.

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

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

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

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

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

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{\sqrt{6}\sqrt{10}}{5} ni -\frac{1}{8} ga ko‘paytiring.

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

\frac{-\sqrt{6}\sqrt{10}}{5\times 8}\sqrt{15} ni yagona kasrga aylantiring.

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

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

$$\frac{-\sqrt{60}\sqrt{15}}{5\times 8}$$

Faktor: 60=15\times 4. \sqrt{15\times 4} koʻpaytmasining kvadrat ildizini \sqrt{15}\sqrt{4} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing.

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

15 hosil qilish uchun \sqrt{15} va \sqrt{15} ni ko'paytirish.

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

40 hosil qilish uchun 5 va 8 ni ko'paytirish.

$$\frac{-15\sqrt{4}}{40}$$

4 ning kvadrat ildizini hisoblab, 2 natijaga ega bo‘ling.

$$\frac{-15\times 2}{40}$$

-30 hosil qilish uchun -15 va 2 ni ko'paytirish.

$$\frac{-30}{40}$$

\frac{-30}{40} ulushini 10 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$-\frac{3}{4}$$

Omil

$$-\frac{3}{4} = -0,75$$