3sqrt{1-2/3+{left(1/2right)}^3} eching

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

Baholash

$$\frac{\sqrt{66}}{4}\approx 2,031009601$$

Yechim qadamlari

1 ni \frac{3}{3} kasrga o‘giring.

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

\frac{3}{3} va \frac{2}{3} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

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

1 olish uchun 3 dan 2 ni ayirish.

$$3\sqrt{\frac{1}{3}+\left(\frac{1}{2}\right)^{3}}$$

3 daraja ko‘rsatkichini \frac{1}{2} ga hisoblang va \frac{1}{8} ni qiymatni oling.

$$3\sqrt{\frac{1}{3}+\frac{1}{8}}$$

3 va 8 ning eng kichik umumiy karralisi 24 ga teng. \frac{1}{3} va \frac{1}{8} ni 24 maxraj bilan kasrlarga aylantirib oling.

$$3\sqrt{\frac{8}{24}+\frac{3}{24}}$$

\frac{8}{24} va \frac{3}{24} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$3\sqrt{\frac{8+3}{24}}$$

11 olish uchun 8 va 3'ni qo'shing.

$$3\sqrt{\frac{11}{24}}$$

\sqrt{\frac{11}{24}} boʻlinmasining kvadrat ildizini \frac{\sqrt{11}}{\sqrt{24}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

$$3\times \frac{\sqrt{11}}{\sqrt{24}}$$

Faktor: 24=2^{2}\times 6. \sqrt{2^{2}\times 6} koʻpaytmasining kvadrat ildizini \sqrt{2^{2}}\sqrt{6} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 2^{2} ning kvadrat ildizini chiqarish.

$$3\times \frac{\sqrt{11}}{2\sqrt{6}}$$

\frac{\sqrt{11}}{2\sqrt{6}} maxrajini \sqrt{6} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$3\times \frac{\sqrt{11}\sqrt{6}}{2\left(\sqrt{6}\right)^{2}}$$

\sqrt{6} kvadrati – 6.

$$3\times \frac{\sqrt{11}\sqrt{6}}{2\times 6}$$

\sqrt{11} va \sqrt{6} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$3\times \frac{\sqrt{66}}{2\times 6}$$

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

$$3\times \frac{\sqrt{66}}{12}$$

3 va 12 ichida eng katta umumiy 12 faktorini bekor qiling.

$$\frac{\sqrt{66}}{4}$$