(3sqrt{6}+sqrt{30})divsqrt{6} eching

$$(3 \sqrt{ 6 } + \sqrt{ 30 } ) \div \sqrt{ 6 }$$

Baholash

$$\sqrt{5}+3\approx 5,236067977$$

Yechim qadamlari

\frac{3\sqrt{6}+\sqrt{30}}{\sqrt{6}} maxrajini \sqrt{6} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{\left(3\sqrt{6}+\sqrt{30}\right)\sqrt{6}}{\left(\sqrt{6}\right)^{2}}$$

\sqrt{6} kvadrati – 6.

$$\frac{\left(3\sqrt{6}+\sqrt{30}\right)\sqrt{6}}{6}$$

3\sqrt{6}+\sqrt{30} ga \sqrt{6} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{3\left(\sqrt{6}\right)^{2}+\sqrt{30}\sqrt{6}}{6}$$

\sqrt{6} kvadrati – 6.

$$\frac{3\times 6+\sqrt{30}\sqrt{6}}{6}$$

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

$$\frac{18+\sqrt{30}\sqrt{6}}{6}$$

Faktor: 30=6\times 5. \sqrt{6\times 5} koʻpaytmasining kvadrat ildizini \sqrt{6}\sqrt{5} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing.

$$\frac{18+\sqrt{6}\sqrt{5}\sqrt{6}}{6}$$

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

$$\frac{18+6\sqrt{5}}{6}$$

3+\sqrt{5} natijani olish uchun 18+6\sqrt{5} ning har bir ifodasini 6 ga bo‘ling.

$$3+\sqrt{5}$$