-5sqrt{8/27}*sqrt{11/4}*(-3sqrt{54}) eching

$$- 5 \sqrt { \frac { 8 } { 27 } } \times \sqrt { 1 \frac { 1 } { 4 } } \times ( - 3 \sqrt { 54 } )$$

Baholash

$$30\sqrt{5}\approx 67,082039325$$

Yechim qadamlari

\sqrt{\frac{8}{27}} boʻlinmasining kvadrat ildizini \frac{\sqrt{8}}{\sqrt{27}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

$$-5\times \frac{\sqrt{8}}{\sqrt{27}}\sqrt{\frac{4+1}{4}}\left(-3\right)\sqrt{54}$$

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.

$$-5\times \frac{2\sqrt{2}}{\sqrt{27}}\sqrt{\frac{4+1}{4}}\left(-3\right)\sqrt{54}$$

Faktor: 27=3^{2}\times 3. \sqrt{3^{2}\times 3} koʻpaytmasining kvadrat ildizini \sqrt{3^{2}}\sqrt{3} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 3^{2} ning kvadrat ildizini chiqarish.

$$-5\times \frac{2\sqrt{2}}{3\sqrt{3}}\sqrt{\frac{4+1}{4}}\left(-3\right)\sqrt{54}$$

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

$$-5\times \frac{2\sqrt{2}\sqrt{3}}{3\left(\sqrt{3}\right)^{2}}\sqrt{\frac{4+1}{4}}\left(-3\right)\sqrt{54}$$

\sqrt{3} kvadrati – 3.

$$-5\times \frac{2\sqrt{2}\sqrt{3}}{3\times 3}\sqrt{\frac{4+1}{4}}\left(-3\right)\sqrt{54}$$

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

$$-5\times \frac{2\sqrt{6}}{3\times 3}\sqrt{\frac{4+1}{4}}\left(-3\right)\sqrt{54}$$

9 hosil qilish uchun 3 va 3 ni ko'paytirish.

$$-5\times \frac{2\sqrt{6}}{9}\sqrt{\frac{4+1}{4}}\left(-3\right)\sqrt{54}$$

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

$$-5\times \frac{2\sqrt{6}}{9}\sqrt{\frac{5}{4}}\left(-3\right)\sqrt{54}$$

\sqrt{\frac{5}{4}} boʻlinmasining kvadrat ildizini \frac{\sqrt{5}}{\sqrt{4}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

$$-5\times \frac{2\sqrt{6}}{9}\times \frac{\sqrt{5}}{\sqrt{4}}\left(-3\right)\sqrt{54}$$

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

$$-5\times \frac{2\sqrt{6}}{9}\times \frac{\sqrt{5}}{2}\left(-3\right)\sqrt{54}$$

15 hosil qilish uchun -5 va -3 ni ko'paytirish.

$$15\times \frac{2\sqrt{6}}{9}\times \frac{\sqrt{5}}{2}\sqrt{54}$$

Faktor: 54=3^{2}\times 6. \sqrt{3^{2}\times 6} koʻpaytmasining kvadrat ildizini \sqrt{3^{2}}\sqrt{6} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 3^{2} ning kvadrat ildizini chiqarish.

$$15\times \frac{2\sqrt{6}}{9}\times \frac{\sqrt{5}}{2}\times 3\sqrt{6}$$

45 hosil qilish uchun 15 va 3 ni ko'paytirish.

$$45\times \frac{2\sqrt{6}}{9}\times \frac{\sqrt{5}}{2}\sqrt{6}$$

45 va 9 ichida eng katta umumiy 9 faktorini bekor qiling.

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

5\times 2\sqrt{6}\times \frac{\sqrt{5}}{2} ni yagona kasrga aylantiring.

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

2 va 2 ni qisqartiring.

$$5\sqrt{6}\sqrt{5}\sqrt{6}$$

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

$$5\times 6\sqrt{5}$$

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

$$30\sqrt{5}$$