frac{left(sqrt{6}-sqrt{12}right)*sqrt{3}}{sqrt{6}}+sqrt{6} eching

$$\frac{ \left( \sqrt{ 6 } - \sqrt{ 12 } \right) \times \sqrt{ 3 } }{ \sqrt{ 6 } } + \sqrt{ 6 }$$

Baholash

$$\sqrt{3}\approx 1,732050808$$

Yechim qadamlari

Faktor: 12=2^{2}\times 3. \sqrt{2^{2}\times 3} koʻpaytmasining kvadrat ildizini \sqrt{2^{2}}\sqrt{3} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 2^{2} ning kvadrat ildizini chiqarish.

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

\frac{\left(\sqrt{6}-2\sqrt{3}\right)\sqrt{3}}{\sqrt{6}} maxrajini \sqrt{6} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

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

\sqrt{6} kvadrati – 6.

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

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

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

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

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

\left(\sqrt{6}-2\sqrt{3}\right)\times \frac{1}{2}\sqrt{2} ni olish uchun \left(\sqrt{6}-2\sqrt{3}\right)\times 3\sqrt{2} ni 6 ga bo‘ling.

$$\left(\sqrt{6}-2\sqrt{3}\right)\times \frac{1}{2}\sqrt{2}+\sqrt{6}$$

\sqrt{6}-2\sqrt{3} ga \frac{1}{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(\sqrt{6}\times \frac{1}{2}-2\sqrt{3}\times \frac{1}{2}\right)\sqrt{2}+\sqrt{6}$$

-2 ni \frac{1}{2} marotabaga ko'paytirish.

$$\left(\sqrt{6}\times \frac{1}{2}-\sqrt{3}\right)\sqrt{2}+\sqrt{6}$$

\sqrt{6}\times \frac{1}{2}-\sqrt{3} ga \sqrt{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\sqrt{6}\times \frac{1}{2}\sqrt{2}-\sqrt{3}\sqrt{2}+\sqrt{6}$$

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

$$\sqrt{2}\sqrt{3}\times \frac{1}{2}\sqrt{2}-\sqrt{3}\sqrt{2}+\sqrt{6}$$

2 hosil qilish uchun \sqrt{2} va \sqrt{2} ni ko'paytirish.

$$2\times \frac{1}{2}\sqrt{3}-\sqrt{3}\sqrt{2}+\sqrt{6}$$

2 va 2 ni qisqartiring.

$$\sqrt{3}-\sqrt{3}\sqrt{2}+\sqrt{6}$$

\sqrt{3} va \sqrt{2} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

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

0 ni olish uchun -\sqrt{6} va \sqrt{6} ni birlashtirish.

$$\sqrt{3}$$