4/4sqrt{2}*frac{sqrt{3}}{sqrt{2}}= eching

$$\frac { 4 } { 4 \sqrt { 2 } } \times \frac { \sqrt { 3 } } { \sqrt { 2 } } =$$

Baholash

$$\frac{\sqrt{3}}{2}\approx 0,866025404$$

Yechim qadamlari

\frac{4}{4\sqrt{2}} maxrajini \sqrt{2} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

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

\sqrt{2} kvadrati – 2.

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

Surat va maxrajdagi ikkala 4 ni qisqartiring.

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

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

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

\sqrt{2} kvadrati – 2.

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

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

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

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

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

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

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

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

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

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

$$\frac{2\sqrt{3}}{4}$$

\frac{1}{2}\sqrt{3} ni olish uchun 2\sqrt{3} ni 4 ga bo‘ling.

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