2sqrt{3}-1/2*sqrt{5}*sqrt{3}divsqrt{20} eching

$$2 \sqrt { 3 } - \frac { 1 } { 2 } \times \sqrt { 5 } \times \sqrt { 3 } \div \sqrt { 20 }$$

Baholash

$$\frac{7\sqrt{3}}{4}\approx 3,031088913$$

Yechim qadamlari

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

$$2\sqrt{3}-\frac{\frac{1}{2}\sqrt{15}}{\sqrt{20}}$$

Faktor: 20=2^{2}\times 5. \sqrt{2^{2}\times 5} koʻpaytmasining kvadrat ildizini \sqrt{2^{2}}\sqrt{5} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 2^{2} ning kvadrat ildizini chiqarish.

$$2\sqrt{3}-\frac{\frac{1}{2}\sqrt{15}}{2\sqrt{5}}$$

\frac{\frac{1}{2}\sqrt{15}}{2\sqrt{5}} maxrajini \sqrt{5} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$2\sqrt{3}-\frac{\frac{1}{2}\sqrt{15}\sqrt{5}}{2\left(\sqrt{5}\right)^{2}}$$

\sqrt{5} kvadrati – 5.

$$2\sqrt{3}-\frac{\frac{1}{2}\sqrt{15}\sqrt{5}}{2\times 5}$$

Faktor: 15=5\times 3. \sqrt{5\times 3} koʻpaytmasining kvadrat ildizini \sqrt{5}\sqrt{3} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing.

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

5 hosil qilish uchun \sqrt{5} va \sqrt{5} ni ko'paytirish.

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

10 hosil qilish uchun 2 va 5 ni ko'paytirish.

$$2\sqrt{3}-\frac{\frac{1}{2}\times 5\sqrt{3}}{10}$$

\frac{5}{2} hosil qilish uchun \frac{1}{2} va 5 ni ko'paytirish.

$$2\sqrt{3}-\frac{\frac{5}{2}\sqrt{3}}{10}$$

\frac{1}{4}\sqrt{3} ni olish uchun \frac{5}{2}\sqrt{3} ni 10 ga bo‘ling.

$$2\sqrt{3}-\frac{1}{4}\sqrt{3}$$

\frac{7}{4}\sqrt{3} ni olish uchun 2\sqrt{3} va -\frac{1}{4}\sqrt{3} ni birlashtirish.

$$\frac{7}{4}\sqrt{3}$$