sqrt{3/4}*(-sqrt{22/3})*sqrt{56} eching

$$\sqrt { \frac { 3 } { 4 } } \times ( - \sqrt { 2 \frac { 2 } { 3 } } ) \times \sqrt { 56 }$$

Baholash

$$-4\sqrt{7}\approx -10,583005244$$

Yechim qadamlari

\sqrt{\frac{3}{4}} boʻlinmasining kvadrat ildizini \frac{\sqrt{3}}{\sqrt{4}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

$$\frac{\sqrt{3}}{\sqrt{4}}\left(-\sqrt{\frac{2\times 3+2}{3}}\right)\sqrt{56}$$

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

$$\frac{\sqrt{3}}{2}\left(-\sqrt{\frac{2\times 3+2}{3}}\right)\sqrt{56}$$

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

$$\frac{\sqrt{3}}{2}\left(-\sqrt{\frac{6+2}{3}}\right)\sqrt{56}$$

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

$$\frac{\sqrt{3}}{2}\left(-\sqrt{\frac{8}{3}}\right)\sqrt{56}$$

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

$$\frac{\sqrt{3}}{2}\left(-\frac{\sqrt{8}}{\sqrt{3}}\right)\sqrt{56}$$

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.

$$\frac{\sqrt{3}}{2}\left(-\frac{2\sqrt{2}}{\sqrt{3}}\right)\sqrt{56}$$

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

$$\frac{\sqrt{3}}{2}\left(-\frac{2\sqrt{2}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\right)\sqrt{56}$$

\sqrt{3} kvadrati – 3.

$$\frac{\sqrt{3}}{2}\left(-\frac{2\sqrt{2}\sqrt{3}}{3}\right)\sqrt{56}$$

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

$$\frac{\sqrt{3}}{2}\left(-\frac{2\sqrt{6}}{3}\right)\sqrt{56}$$

Faktor: 56=2^{2}\times 14. \sqrt{2^{2}\times 14} koʻpaytmasining kvadrat ildizini \sqrt{2^{2}}\sqrt{14} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 2^{2} ning kvadrat ildizini chiqarish.

$$\frac{\sqrt{3}}{2}\left(-\frac{2\sqrt{6}}{3}\right)\times 2\sqrt{14}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{\sqrt{3}}{2} ni -\frac{2\sqrt{6}}{3} ga ko‘paytiring.

$$\frac{-\sqrt{3}\times 2\sqrt{6}}{2\times 3}\times 2\sqrt{14}$$

Surat va maxrajdagi ikkala 2 ni qisqartiring.

$$\frac{-\sqrt{3}\sqrt{6}}{3}\times 2\sqrt{14}$$

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

$$\frac{-\sqrt{3}\sqrt{6}\times 2}{3}\sqrt{14}$$

\frac{-\sqrt{3}\sqrt{6}\times 2}{3}\sqrt{14} ni yagona kasrga aylantiring.

$$\frac{-\sqrt{3}\sqrt{6}\times 2\sqrt{14}}{3}$$

Faktor: 6=3\times 2. \sqrt{3\times 2} koʻpaytmasining kvadrat ildizini \sqrt{3}\sqrt{2} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing.

$$\frac{-\sqrt{3}\sqrt{3}\sqrt{2}\times 2\sqrt{14}}{3}$$

3 hosil qilish uchun \sqrt{3} va \sqrt{3} ni ko'paytirish.

$$\frac{-3\sqrt{2}\times 2\sqrt{14}}{3}$$

Faktor: 14=2\times 7. \sqrt{2\times 7} koʻpaytmasining kvadrat ildizini \sqrt{2}\sqrt{7} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing.

$$\frac{-3\sqrt{2}\times 2\sqrt{2}\sqrt{7}}{3}$$

2 hosil qilish uchun \sqrt{2} va \sqrt{2} ni ko'paytirish.

$$\frac{-3\times 2\times 2\sqrt{7}}{3}$$

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

$$\frac{-6\times 2\sqrt{7}}{3}$$

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

$$\frac{-12\sqrt{7}}{3}$$

-4\sqrt{7} ni olish uchun -12\sqrt{7} ni 3 ga bo‘ling.

$$-4\sqrt{7}$$