12sqrt{1/6}div3sqrt{7/12}*1/2sqrt{101/2} eching

$$12 \sqrt { \frac { 1 } { 6 } } \div 3 \sqrt { \frac { 7 } { 12 } } \times \frac { 1 } { 2 } \sqrt { 10 \frac { 1 } { 2 } }$$

Baholash

$$\frac{7\sqrt{3}}{6}\approx 2,020725942$$

Yechim qadamlari

\sqrt{\frac{1}{6}} boʻlinmasining kvadrat ildizini \frac{\sqrt{1}}{\sqrt{6}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

$$\frac{12\times \frac{\sqrt{1}}{\sqrt{6}}}{3}\sqrt{\frac{7}{12}}\times \frac{1}{2}\sqrt{\frac{10\times 2+1}{2}}$$

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

$$\frac{12\times \frac{1}{\sqrt{6}}}{3}\sqrt{\frac{7}{12}}\times \frac{1}{2}\sqrt{\frac{10\times 2+1}{2}}$$

\frac{1}{\sqrt{6}} maxrajini \sqrt{6} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{12\times \frac{\sqrt{6}}{\left(\sqrt{6}\right)^{2}}}{3}\sqrt{\frac{7}{12}}\times \frac{1}{2}\sqrt{\frac{10\times 2+1}{2}}$$

\sqrt{6} kvadrati – 6.

$$\frac{12\times \frac{\sqrt{6}}{6}}{3}\sqrt{\frac{7}{12}}\times \frac{1}{2}\sqrt{\frac{10\times 2+1}{2}}$$

12 va 6 ichida eng katta umumiy 6 faktorini bekor qiling.

$$\frac{2\sqrt{6}}{3}\sqrt{\frac{7}{12}}\times \frac{1}{2}\sqrt{\frac{10\times 2+1}{2}}$$

\sqrt{\frac{7}{12}} boʻlinmasining kvadrat ildizini \frac{\sqrt{7}}{\sqrt{12}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

$$\frac{2\sqrt{6}}{3}\times \frac{\sqrt{7}}{\sqrt{12}}\times \frac{1}{2}\sqrt{\frac{10\times 2+1}{2}}$$

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.

$$\frac{2\sqrt{6}}{3}\times \frac{\sqrt{7}}{2\sqrt{3}}\times \frac{1}{2}\sqrt{\frac{10\times 2+1}{2}}$$

\frac{\sqrt{7}}{2\sqrt{3}} maxrajini \sqrt{3} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{2\sqrt{6}}{3}\times \frac{\sqrt{7}\sqrt{3}}{2\left(\sqrt{3}\right)^{2}}\times \frac{1}{2}\sqrt{\frac{10\times 2+1}{2}}$$

\sqrt{3} kvadrati – 3.

$$\frac{2\sqrt{6}}{3}\times \frac{\sqrt{7}\sqrt{3}}{2\times 3}\times \frac{1}{2}\sqrt{\frac{10\times 2+1}{2}}$$

\sqrt{7} va \sqrt{3} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$\frac{2\sqrt{6}}{3}\times \frac{\sqrt{21}}{2\times 3}\times \frac{1}{2}\sqrt{\frac{10\times 2+1}{2}}$$

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

$$\frac{2\sqrt{6}}{3}\times \frac{\sqrt{21}}{6}\times \frac{1}{2}\sqrt{\frac{10\times 2+1}{2}}$$

20 hosil qilish uchun 10 va 2 ni ko'paytirish.

$$\frac{2\sqrt{6}}{3}\times \frac{\sqrt{21}}{6}\times \frac{1}{2}\sqrt{\frac{20+1}{2}}$$

21 olish uchun 20 va 1'ni qo'shing.

$$\frac{2\sqrt{6}}{3}\times \frac{\sqrt{21}}{6}\times \frac{1}{2}\sqrt{\frac{21}{2}}$$

\sqrt{\frac{21}{2}} boʻlinmasining kvadrat ildizini \frac{\sqrt{21}}{\sqrt{2}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

$$\frac{2\sqrt{6}}{3}\times \frac{\sqrt{21}}{6}\times \frac{1}{2}\times \frac{\sqrt{21}}{\sqrt{2}}$$

\frac{\sqrt{21}}{\sqrt{2}} maxrajini \sqrt{2} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{2\sqrt{6}}{3}\times \frac{\sqrt{21}}{6}\times \frac{1}{2}\times \frac{\sqrt{21}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

\sqrt{2} kvadrati – 2.

$$\frac{2\sqrt{6}}{3}\times \frac{\sqrt{21}}{6}\times \frac{1}{2}\times \frac{\sqrt{21}\sqrt{2}}{2}$$

\sqrt{21} va \sqrt{2} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$\frac{2\sqrt{6}}{3}\times \frac{\sqrt{21}}{6}\times \frac{1}{2}\times \frac{\sqrt{42}}{2}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{2\sqrt{6}}{3} ni \frac{\sqrt{21}}{6} ga ko‘paytiring.

$$\frac{2\sqrt{6}\sqrt{21}}{3\times 6}\times \frac{1}{2}\times \frac{\sqrt{42}}{2}$$

Surat va maxrajdagi ikkala 2 ni qisqartiring.

$$\frac{\sqrt{6}\sqrt{21}}{3\times 3}\times \frac{1}{2}\times \frac{\sqrt{42}}{2}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{\sqrt{6}\sqrt{21}}{3\times 3} ni \frac{1}{2} ga ko‘paytiring.

$$\frac{\sqrt{6}\sqrt{21}}{3\times 3\times 2}\times \frac{\sqrt{42}}{2}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{\sqrt{6}\sqrt{21}}{3\times 3\times 2} ni \frac{\sqrt{42}}{2} ga ko‘paytiring.

$$\frac{\sqrt{6}\sqrt{21}\sqrt{42}}{3\times 3\times 2\times 2}$$

Faktor: 42=6\times 7. \sqrt{6\times 7} koʻpaytmasining kvadrat ildizini \sqrt{6}\sqrt{7} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing.

$$\frac{\sqrt{6}\sqrt{21}\sqrt{6}\sqrt{7}}{3\times 3\times 2\times 2}$$

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

$$\frac{6\sqrt{21}\sqrt{7}}{3\times 3\times 2\times 2}$$

Faktor: 21=7\times 3. \sqrt{7\times 3} koʻpaytmasining kvadrat ildizini \sqrt{7}\sqrt{3} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing.

$$\frac{6\sqrt{7}\sqrt{3}\sqrt{7}}{3\times 3\times 2\times 2}$$

7 hosil qilish uchun \sqrt{7} va \sqrt{7} ni ko'paytirish.

$$\frac{6\times 7\sqrt{3}}{3\times 3\times 2\times 2}$$

42 hosil qilish uchun 6 va 7 ni ko'paytirish.

$$\frac{42\sqrt{3}}{3\times 3\times 2\times 2}$$

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

$$\frac{42\sqrt{3}}{9\times 2\times 2}$$

18 hosil qilish uchun 9 va 2 ni ko'paytirish.

$$\frac{42\sqrt{3}}{18\times 2}$$

36 hosil qilish uchun 18 va 2 ni ko'paytirish.

$$\frac{42\sqrt{3}}{36}$$

\frac{7}{6}\sqrt{3} ni olish uchun 42\sqrt{3} ni 36 ga bo‘ling.

$$\frac{7}{6}\sqrt{3}$$