5sqrt{3}+2sqrt{27}+1/sqrt{3} eching

$$5 \sqrt { 3 } + 2 \sqrt { 27 } + \frac { 1 } { \sqrt { 3 } }$$

Baholash

$$\frac{34\sqrt{3}}{3}\approx 19,629909152$$

Yechim qadamlari

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.

$$5\sqrt{3}+2\times 3\sqrt{3}+\frac{1}{\sqrt{3}}$$

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

$$5\sqrt{3}+6\sqrt{3}+\frac{1}{\sqrt{3}}$$

11\sqrt{3} ni olish uchun 5\sqrt{3} va 6\sqrt{3} ni birlashtirish.

$$11\sqrt{3}+\frac{1}{\sqrt{3}}$$

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

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

\sqrt{3} kvadrati – 3.

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

\frac{34}{3}\sqrt{3} ni olish uchun 11\sqrt{3} va \frac{\sqrt{3}}{3} ni birlashtirish.

$$\frac{34}{3}\sqrt{3}$$