sqrt{75}*frac{sqrt{6}}{3}div1/sqrt{2} eching

$$\sqrt { 75 } \times \frac { \sqrt { 6 } } { 3 } \div \frac { 1 } { \sqrt { 2 } }$$

Baholash

$$10$$

Yechim qadamlari

Faktor: 75=5^{2}\times 3. \sqrt{5^{2}\times 3} koʻpaytmasining kvadrat ildizini \sqrt{5^{2}}\sqrt{3} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 5^{2} ning kvadrat ildizini chiqarish.

$$\frac{5\sqrt{3}\times \frac{\sqrt{6}}{3}}{\frac{1}{\sqrt{2}}}$$

5\times \frac{\sqrt{6}}{3} ni yagona kasrga aylantiring.

$$\frac{\frac{5\sqrt{6}}{3}\sqrt{3}}{\frac{1}{\sqrt{2}}}$$

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

$$\frac{\frac{5\sqrt{6}}{3}\sqrt{3}}{\frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}}$$

\sqrt{2} kvadrati – 2.

$$\frac{\frac{5\sqrt{6}}{3}\sqrt{3}}{\frac{\sqrt{2}}{2}}$$

\frac{5\sqrt{6}}{3}\sqrt{3} ni yagona kasrga aylantiring.

$$\frac{\frac{5\sqrt{6}\sqrt{3}}{3}}{\frac{\sqrt{2}}{2}}$$

\frac{5\sqrt{6}\sqrt{3}}{3} ni \frac{\sqrt{2}}{2} ga bo'lish \frac{5\sqrt{6}\sqrt{3}}{3} ga k'paytirish \frac{\sqrt{2}}{2} ga qaytarish.

$$\frac{5\sqrt{6}\sqrt{3}\times 2}{3\sqrt{2}}$$

\frac{5\sqrt{6}\sqrt{3}\times 2}{3\sqrt{2}} maxrajini \sqrt{2} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{5\sqrt{6}\sqrt{3}\times 2\sqrt{2}}{3\left(\sqrt{2}\right)^{2}}$$

\sqrt{2} kvadrati – 2.

$$\frac{5\sqrt{6}\sqrt{3}\times 2\sqrt{2}}{3\times 2}$$

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

$$\frac{5\sqrt{3}\sqrt{2}\sqrt{3}\times 2\sqrt{2}}{3\times 2}$$

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

$$\frac{5\times 3\sqrt{2}\times 2\sqrt{2}}{3\times 2}$$

15 hosil qilish uchun 5 va 3 ni ko'paytirish.

$$\frac{15\sqrt{2}\times 2\sqrt{2}}{3\times 2}$$

30 hosil qilish uchun 15 va 2 ni ko'paytirish.

$$\frac{30\sqrt{2}\sqrt{2}}{3\times 2}$$

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

$$\frac{30\times 2}{3\times 2}$$

60 hosil qilish uchun 30 va 2 ni ko'paytirish.

$$\frac{60}{3\times 2}$$

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

$$\frac{60}{6}$$

10 ni olish uchun 60 ni 6 ga bo‘ling.

$$10$$

Omil

$$2\times 5$$