frac{sqrt{6}+3sqrt{3}}{sqrt{3}} eching

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

Baholash

$$\sqrt{2}+3\approx 4,414213562$$

Yechim qadamlari

\frac{\sqrt{6}+3\sqrt{3}}{\sqrt{3}} maxrajini \sqrt{3} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

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

\sqrt{3} kvadrati – 3.

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

\sqrt{6}+3\sqrt{3} ga \sqrt{3} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

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

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

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

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

\sqrt{3} kvadrati – 3.

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

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

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

\sqrt{2}+3 natijani olish uchun 3\sqrt{2}+9 ning har bir ifodasini 3 ga bo‘ling.

$$\sqrt{2}+3$$