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

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

Baholash

$$-3$$

Yechim qadamlari

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

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

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

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

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

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

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.

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

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

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

\sqrt{3} kvadrati – 3.

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

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

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

3 va 3 ni qisqartiring.

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

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

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

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

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

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

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

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

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

\sqrt{5} kvadrati – 5.

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

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

$$4\sqrt{6}\times \frac{\sqrt{10}}{5}\left(-\frac{1}{8}\right)\sqrt{15}$$

4\left(-\frac{1}{8}\right) ni yagona kasrga aylantiring.

$$\frac{4\left(-1\right)}{8}\sqrt{6}\times \frac{\sqrt{10}}{5}\sqrt{15}$$

-4 hosil qilish uchun 4 va -1 ni ko'paytirish.

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

\frac{-4}{8} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$-\frac{1}{2}\sqrt{6}\times \frac{\sqrt{10}}{5}\sqrt{15}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali -\frac{1}{2} ni \frac{\sqrt{10}}{5} ga ko‘paytiring.

$$\frac{-\sqrt{10}}{2\times 5}\sqrt{6}\sqrt{15}$$

\frac{-\sqrt{10}}{2\times 5}\sqrt{15} ni yagona kasrga aylantiring.

$$\frac{-\sqrt{10}\sqrt{15}}{2\times 5}\sqrt{6}$$

\sqrt{10} va \sqrt{15} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$\frac{-\sqrt{150}}{2\times 5}\sqrt{6}$$

10 hosil qilish uchun 2 va 5 ni ko'paytirish.

$$\frac{-\sqrt{150}}{10}\sqrt{6}$$

Faktor: 150=5^{2}\times 6. \sqrt{5^{2}\times 6} koʻpaytmasining kvadrat ildizini \sqrt{5^{2}}\sqrt{6} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 5^{2} ning kvadrat ildizini chiqarish.

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

-\frac{1}{2}\sqrt{6} ni olish uchun -5\sqrt{6} ni 10 ga bo‘ling.

$$-\frac{1}{2}\sqrt{6}\sqrt{6}$$

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

$$-\frac{1}{2}\times 6$$

-\frac{1}{2}\times 6 ni yagona kasrga aylantiring.

$$\frac{-6}{2}$$

-3 ni olish uchun -6 ni 2 ga bo‘ling.

$$-3$$

Omil

$$-3$$