(4sqrt{6}-4sqrt{1/2}+3sqrt{8})div2sqrt{2}= eching

$$( 4 \sqrt { 6 } - 4 \sqrt { \frac { 1 } { 2 } } + 3 \sqrt { 8 } ) \div 2 \sqrt { 2 } =$$

Baholash

$$4\left(\sqrt{3}+1\right)\approx 10,92820323$$

Yechim qadamlari

\sqrt{\frac{1}{2}} boʻlinmasining kvadrat ildizini \frac{\sqrt{1}}{\sqrt{2}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

$$\frac{4\sqrt{6}-4\times \frac{\sqrt{1}}{\sqrt{2}}+3\sqrt{8}}{2}\sqrt{2}$$

1 ning kvadrat ildizini hisoblab, 1 natijaga ega bo‘ling.

$$\frac{4\sqrt{6}-4\times \frac{1}{\sqrt{2}}+3\sqrt{8}}{2}\sqrt{2}$$

\frac{1}{\sqrt{2}} maxrajini \sqrt{2} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{4\sqrt{6}-4\times \frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}+3\sqrt{8}}{2}\sqrt{2}$$

\sqrt{2} kvadrati – 2.

$$\frac{4\sqrt{6}-4\times \frac{\sqrt{2}}{2}+3\sqrt{8}}{2}\sqrt{2}$$

4 va 2 ichida eng katta umumiy 2 faktorini bekor qiling.

$$\frac{4\sqrt{6}-2\sqrt{2}+3\sqrt{8}}{2}\sqrt{2}$$

Faktor: 8=2^{2}\times 2. \sqrt{2^{2}\times 2} koʻpaytmasining kvadrat ildizini \sqrt{2^{2}}\sqrt{2} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 2^{2} ning kvadrat ildizini chiqarish.

$$\frac{4\sqrt{6}-2\sqrt{2}+3\times 2\sqrt{2}}{2}\sqrt{2}$$

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

$$\frac{4\sqrt{6}-2\sqrt{2}+6\sqrt{2}}{2}\sqrt{2}$$

4\sqrt{2} ni olish uchun -2\sqrt{2} va 6\sqrt{2} ni birlashtirish.

$$\frac{4\sqrt{6}+4\sqrt{2}}{2}\sqrt{2}$$

\frac{4\sqrt{6}+4\sqrt{2}}{2}\sqrt{2} ni yagona kasrga aylantiring.

$$\frac{\left(4\sqrt{6}+4\sqrt{2}\right)\sqrt{2}}{2}$$

4\sqrt{6}+4\sqrt{2} ga \sqrt{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{4\sqrt{6}\sqrt{2}+4\left(\sqrt{2}\right)^{2}}{2}$$

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

$$\frac{4\sqrt{2}\sqrt{3}\sqrt{2}+4\left(\sqrt{2}\right)^{2}}{2}$$

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

$$\frac{4\times 2\sqrt{3}+4\left(\sqrt{2}\right)^{2}}{2}$$

8 hosil qilish uchun 4 va 2 ni ko'paytirish.

$$\frac{8\sqrt{3}+4\left(\sqrt{2}\right)^{2}}{2}$$

\sqrt{2} kvadrati – 2.

$$\frac{8\sqrt{3}+4\times 2}{2}$$

8 hosil qilish uchun 4 va 2 ni ko'paytirish.

$$\frac{8\sqrt{3}+8}{2}$$