2sqrt{1/27}-2/3sqrt{18}-sqrt{4/3}-4sqrt{1/2} eching

$$2 \sqrt{ \frac{ 1 }{ 27 } } - \frac{ 2 }{ 3 } \sqrt{ 18 } - \sqrt{ \frac{ 4 }{ 3 } } -4 \sqrt{ \frac{ 1 }{ 2 } }$$

Baholash

$$-\frac{4\sqrt{3}}{9}-4\sqrt{2}\approx -6,426654608$$

Qisqa yechim qadamlari

\sqrt{\frac{1}{27}} boʻlinmasining kvadrat ildizini \frac{\sqrt{1}}{\sqrt{27}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

$$2\times \frac{\sqrt{1}}{\sqrt{27}}-\frac{2}{3}\sqrt{18}-\sqrt{\frac{4}{3}}-4\sqrt{\frac{1}{2}}$$

1 ning kvadrat ildizini hisoblab, 1 natijaga ega bo‘ling.

$$2\times \frac{1}{\sqrt{27}}-\frac{2}{3}\sqrt{18}-\sqrt{\frac{4}{3}}-4\sqrt{\frac{1}{2}}$$

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.

$$2\times \frac{1}{3\sqrt{3}}-\frac{2}{3}\sqrt{18}-\sqrt{\frac{4}{3}}-4\sqrt{\frac{1}{2}}$$

\frac{1}{3\sqrt{3}} maxrajini \sqrt{3} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$2\times \frac{\sqrt{3}}{3\left(\sqrt{3}\right)^{2}}-\frac{2}{3}\sqrt{18}-\sqrt{\frac{4}{3}}-4\sqrt{\frac{1}{2}}$$

\sqrt{3} kvadrati – 3.

$$2\times \frac{\sqrt{3}}{3\times 3}-\frac{2}{3}\sqrt{18}-\sqrt{\frac{4}{3}}-4\sqrt{\frac{1}{2}}$$

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

$$2\times \frac{\sqrt{3}}{9}-\frac{2}{3}\sqrt{18}-\sqrt{\frac{4}{3}}-4\sqrt{\frac{1}{2}}$$

2\times \frac{\sqrt{3}}{9} ni yagona kasrga aylantiring.

$$\frac{2\sqrt{3}}{9}-\frac{2}{3}\sqrt{18}-\sqrt{\frac{4}{3}}-4\sqrt{\frac{1}{2}}$$

Faktor: 18=3^{2}\times 2. \sqrt{3^{2}\times 2} koʻpaytmasining kvadrat ildizini \sqrt{3^{2}}\sqrt{2} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 3^{2} ning kvadrat ildizini chiqarish.

$$\frac{2\sqrt{3}}{9}-\frac{2}{3}\times 3\sqrt{2}-\sqrt{\frac{4}{3}}-4\sqrt{\frac{1}{2}}$$

3 va 3 ni qisqartiring.

$$\frac{2\sqrt{3}}{9}-2\sqrt{2}-\sqrt{\frac{4}{3}}-4\sqrt{\frac{1}{2}}$$

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

$$\frac{2\sqrt{3}}{9}-2\sqrt{2}-\frac{\sqrt{4}}{\sqrt{3}}-4\sqrt{\frac{1}{2}}$$

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

$$\frac{2\sqrt{3}}{9}-2\sqrt{2}-\frac{2}{\sqrt{3}}-4\sqrt{\frac{1}{2}}$$

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

$$\frac{2\sqrt{3}}{9}-2\sqrt{2}-\frac{2\sqrt{3}}{\left(\sqrt{3}\right)^{2}}-4\sqrt{\frac{1}{2}}$$

\sqrt{3} kvadrati – 3.

$$\frac{2\sqrt{3}}{9}-2\sqrt{2}-\frac{2\sqrt{3}}{3}-4\sqrt{\frac{1}{2}}$$

\sqrt{\frac{1}{2}} boʻlinmasining kvadrat ildizini \frac{\sqrt{1}}{\sqrt{2}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

$$\frac{2\sqrt{3}}{9}-2\sqrt{2}-\frac{2\sqrt{3}}{3}-4\times \frac{\sqrt{1}}{\sqrt{2}}$$

1 ning kvadrat ildizini hisoblab, 1 natijaga ega bo‘ling.

$$\frac{2\sqrt{3}}{9}-2\sqrt{2}-\frac{2\sqrt{3}}{3}-4\times \frac{1}{\sqrt{2}}$$

\frac{1}{\sqrt{2}} maxrajini \sqrt{2} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

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

\sqrt{2} kvadrati – 2.

$$\frac{2\sqrt{3}}{9}-2\sqrt{2}-\frac{2\sqrt{3}}{3}-4\times \frac{\sqrt{2}}{2}$$

4 va 2 ichida eng katta umumiy 2 faktorini bekor qiling.

$$\frac{2\sqrt{3}}{9}-2\sqrt{2}-\frac{2\sqrt{3}}{3}-2\sqrt{2}$$

-4\sqrt{2} ni olish uchun -2\sqrt{2} va -2\sqrt{2} ni birlashtirish.

$$\frac{2\sqrt{3}}{9}-4\sqrt{2}-\frac{2\sqrt{3}}{3}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. -4\sqrt{2} ni \frac{9}{9} marotabaga ko'paytirish.

$$\frac{2\sqrt{3}}{9}+\frac{9\left(-4\right)\sqrt{2}}{9}-\frac{2\sqrt{3}}{3}$$

\frac{2\sqrt{3}}{9} va \frac{9\left(-4\right)\sqrt{2}}{9} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{2\sqrt{3}+9\left(-4\right)\sqrt{2}}{9}-\frac{2\sqrt{3}}{3}$$

2\sqrt{3}+9\left(-4\right)\sqrt{2} ichidagi ko‘paytirishlarni bajaring.

$$\frac{2\sqrt{3}-36\sqrt{2}}{9}-\frac{2\sqrt{3}}{3}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 9 va 3 ning eng kichik umumiy karralisi 9. \frac{2\sqrt{3}}{3} ni \frac{3}{3} marotabaga ko'paytirish.

$$\frac{2\sqrt{3}-36\sqrt{2}}{9}-\frac{3\times 2\sqrt{3}}{9}$$

\frac{2\sqrt{3}-36\sqrt{2}}{9} va \frac{3\times 2\sqrt{3}}{9} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{2\sqrt{3}-36\sqrt{2}-3\times 2\sqrt{3}}{9}$$

2\sqrt{3}-36\sqrt{2}-3\times 2\sqrt{3} ichidagi ko‘paytirishlarni bajaring.

$$\frac{2\sqrt{3}-36\sqrt{2}-6\sqrt{3}}{9}$$

2\sqrt{3}-36\sqrt{2}-6\sqrt{3} hisob-kitobini qiling.

$$\frac{-4\sqrt{3}-36\sqrt{2}}{9}$$

Omil

$$\frac{4 {(-\sqrt{3} - 9 \sqrt{2})}}{9} = -6,426654608411882$$