(sqrt{2}-2)^2+sqrt{12/3}divsqrt{5/24} eching

$$( \sqrt { 2 } - 2 ) ^ { 2 } + \sqrt { 1 \frac { 2 } { 3 } } \div \sqrt { \frac { 5 } { 24 } }$$

Baholash

$$6-2\sqrt{2}\approx 3,171572875$$

Yechim qadamlari

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(\sqrt{2}-2\right)^{2} kengaytirilishi uchun ishlating.

$$\left(\sqrt{2}\right)^{2}-4\sqrt{2}+4+\frac{\sqrt{\frac{1\times 3+2}{3}}}{\sqrt{\frac{5}{24}}}$$

\sqrt{2} kvadrati – 2.

$$2-4\sqrt{2}+4+\frac{\sqrt{\frac{1\times 3+2}{3}}}{\sqrt{\frac{5}{24}}}$$

6 olish uchun 2 va 4'ni qo'shing.

$$6-4\sqrt{2}+\frac{\sqrt{\frac{1\times 3+2}{3}}}{\sqrt{\frac{5}{24}}}$$

3 hosil qilish uchun 1 va 3 ni ko'paytirish.

$$6-4\sqrt{2}+\frac{\sqrt{\frac{3+2}{3}}}{\sqrt{\frac{5}{24}}}$$

5 olish uchun 3 va 2'ni qo'shing.

$$6-4\sqrt{2}+\frac{\sqrt{\frac{5}{3}}}{\sqrt{\frac{5}{24}}}$$

\sqrt{\frac{5}{3}} boʻlinmasining kvadrat ildizini \frac{\sqrt{5}}{\sqrt{3}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

$$6-4\sqrt{2}+\frac{\frac{\sqrt{5}}{\sqrt{3}}}{\sqrt{\frac{5}{24}}}$$

\frac{\sqrt{5}}{\sqrt{3}} maxrajini \sqrt{3} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$6-4\sqrt{2}+\frac{\frac{\sqrt{5}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}}{\sqrt{\frac{5}{24}}}$$

\sqrt{3} kvadrati – 3.

$$6-4\sqrt{2}+\frac{\frac{\sqrt{5}\sqrt{3}}{3}}{\sqrt{\frac{5}{24}}}$$

\sqrt{5} va \sqrt{3} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$6-4\sqrt{2}+\frac{\frac{\sqrt{15}}{3}}{\sqrt{\frac{5}{24}}}$$

\sqrt{\frac{5}{24}} boʻlinmasining kvadrat ildizini \frac{\sqrt{5}}{\sqrt{24}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

$$6-4\sqrt{2}+\frac{\frac{\sqrt{15}}{3}}{\frac{\sqrt{5}}{\sqrt{24}}}$$

Faktor: 24=2^{2}\times 6. \sqrt{2^{2}\times 6} koʻpaytmasining kvadrat ildizini \sqrt{2^{2}}\sqrt{6} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 2^{2} ning kvadrat ildizini chiqarish.

$$6-4\sqrt{2}+\frac{\frac{\sqrt{15}}{3}}{\frac{\sqrt{5}}{2\sqrt{6}}}$$

\frac{\sqrt{5}}{2\sqrt{6}} maxrajini \sqrt{6} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$6-4\sqrt{2}+\frac{\frac{\sqrt{15}}{3}}{\frac{\sqrt{5}\sqrt{6}}{2\left(\sqrt{6}\right)^{2}}}$$

\sqrt{6} kvadrati – 6.

$$6-4\sqrt{2}+\frac{\frac{\sqrt{15}}{3}}{\frac{\sqrt{5}\sqrt{6}}{2\times 6}}$$

\sqrt{5} va \sqrt{6} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$6-4\sqrt{2}+\frac{\frac{\sqrt{15}}{3}}{\frac{\sqrt{30}}{2\times 6}}$$

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

$$6-4\sqrt{2}+\frac{\frac{\sqrt{15}}{3}}{\frac{\sqrt{30}}{12}}$$

\frac{\sqrt{15}}{3} ni \frac{\sqrt{30}}{12} ga bo'lish \frac{\sqrt{15}}{3} ga k'paytirish \frac{\sqrt{30}}{12} ga qaytarish.

$$6-4\sqrt{2}+\frac{\sqrt{15}\times 12}{3\sqrt{30}}$$

Surat va maxrajdagi ikkala 3 ni qisqartiring.

$$6-4\sqrt{2}+\frac{4\sqrt{15}}{\sqrt{30}}$$

\frac{4\sqrt{15}}{\sqrt{30}} maxrajini \sqrt{30} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$6-4\sqrt{2}+\frac{4\sqrt{15}\sqrt{30}}{\left(\sqrt{30}\right)^{2}}$$

\sqrt{30} kvadrati – 30.

$$6-4\sqrt{2}+\frac{4\sqrt{15}\sqrt{30}}{30}$$

Faktor: 30=15\times 2. \sqrt{15\times 2} koʻpaytmasining kvadrat ildizini \sqrt{15}\sqrt{2} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing.

$$6-4\sqrt{2}+\frac{4\sqrt{15}\sqrt{15}\sqrt{2}}{30}$$

15 hosil qilish uchun \sqrt{15} va \sqrt{15} ni ko'paytirish.

$$6-4\sqrt{2}+\frac{4\times 15\sqrt{2}}{30}$$

60 hosil qilish uchun 4 va 15 ni ko'paytirish.

$$6-4\sqrt{2}+\frac{60\sqrt{2}}{30}$$

2\sqrt{2} ni olish uchun 60\sqrt{2} ni 30 ga bo‘ling.

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

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

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