sqrt{15}div(1/sqrt{3}+1/sqrt{5}) eching

$$\sqrt{ 15 } \div ( \frac{ 1 }{ \sqrt{ 3 } } + \frac{ 1 }{ \sqrt{ 5 } } )$$

Baholash

$$\frac{15\left(\sqrt{5}-\sqrt{3}\right)}{2}\approx 3,780128774$$

Qisqa yechim qadamlari

\frac{1}{\sqrt{3}} maxrajini \sqrt{3} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

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

\sqrt{3} kvadrati – 3.

$$\frac{\sqrt{15}}{\frac{\sqrt{3}}{3}+\frac{1}{\sqrt{5}}}$$

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

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

\sqrt{5} kvadrati – 5.

$$\frac{\sqrt{15}}{\frac{\sqrt{3}}{3}+\frac{\sqrt{5}}{5}}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 3 va 5 ning eng kichik umumiy karralisi 15. \frac{\sqrt{3}}{3} ni \frac{5}{5} marotabaga ko'paytirish. \frac{\sqrt{5}}{5} ni \frac{3}{3} marotabaga ko'paytirish.

$$\frac{\sqrt{15}}{\frac{5\sqrt{3}}{15}+\frac{3\sqrt{5}}{15}}$$

\frac{5\sqrt{3}}{15} va \frac{3\sqrt{5}}{15} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\sqrt{15}}{\frac{5\sqrt{3}+3\sqrt{5}}{15}}$$

\sqrt{15} ni \frac{5\sqrt{3}+3\sqrt{5}}{15} ga bo'lish \sqrt{15} ga k'paytirish \frac{5\sqrt{3}+3\sqrt{5}}{15} ga qaytarish.

$$\frac{\sqrt{15}\times 15}{5\sqrt{3}+3\sqrt{5}}$$

\frac{\sqrt{15}\times 15}{5\sqrt{3}+3\sqrt{5}} maxrajini 5\sqrt{3}-3\sqrt{5} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{\sqrt{15}\times 15\left(5\sqrt{3}-3\sqrt{5}\right)}{\left(5\sqrt{3}+3\sqrt{5}\right)\left(5\sqrt{3}-3\sqrt{5}\right)}$$

Hisoblang: \left(5\sqrt{3}+3\sqrt{5}\right)\left(5\sqrt{3}-3\sqrt{5}\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

\left(5\sqrt{3}\right)^{2} ni kengaytirish.

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

2 daraja ko‘rsatkichini 5 ga hisoblang va 25 ni qiymatni oling.

$$\frac{\sqrt{15}\times 15\left(5\sqrt{3}-3\sqrt{5}\right)}{25\left(\sqrt{3}\right)^{2}-\left(3\sqrt{5}\right)^{2}}$$

\sqrt{3} kvadrati – 3.

$$\frac{\sqrt{15}\times 15\left(5\sqrt{3}-3\sqrt{5}\right)}{25\times 3-\left(3\sqrt{5}\right)^{2}}$$

75 hosil qilish uchun 25 va 3 ni ko'paytirish.

$$\frac{\sqrt{15}\times 15\left(5\sqrt{3}-3\sqrt{5}\right)}{75-\left(3\sqrt{5}\right)^{2}}$$

\left(3\sqrt{5}\right)^{2} ni kengaytirish.

$$\frac{\sqrt{15}\times 15\left(5\sqrt{3}-3\sqrt{5}\right)}{75-3^{2}\left(\sqrt{5}\right)^{2}}$$

2 daraja ko‘rsatkichini 3 ga hisoblang va 9 ni qiymatni oling.

$$\frac{\sqrt{15}\times 15\left(5\sqrt{3}-3\sqrt{5}\right)}{75-9\left(\sqrt{5}\right)^{2}}$$

\sqrt{5} kvadrati – 5.

$$\frac{\sqrt{15}\times 15\left(5\sqrt{3}-3\sqrt{5}\right)}{75-9\times 5}$$

45 hosil qilish uchun 9 va 5 ni ko'paytirish.

$$\frac{\sqrt{15}\times 15\left(5\sqrt{3}-3\sqrt{5}\right)}{75-45}$$

30 olish uchun 75 dan 45 ni ayirish.

$$\frac{\sqrt{15}\times 15\left(5\sqrt{3}-3\sqrt{5}\right)}{30}$$

\sqrt{15}\times \frac{1}{2}\left(5\sqrt{3}-3\sqrt{5}\right) ni olish uchun \sqrt{15}\times 15\left(5\sqrt{3}-3\sqrt{5}\right) ni 30 ga bo‘ling.

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

\sqrt{15}\times \frac{1}{2} ga 5\sqrt{3}-3\sqrt{5} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

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

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

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

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

\frac{3}{2} hosil qilish uchun 3 va \frac{1}{2} ni ko'paytirish.

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

\frac{3}{2}\times 5 ni yagona kasrga aylantiring.

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

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

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

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

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

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

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

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

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

\frac{5}{2}\left(-3\right) ni yagona kasrga aylantiring.

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

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

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

\frac{-15}{2} kasri manfiy belgini olib tashlash bilan -\frac{15}{2} sifatida qayta yozilishi mumkin.

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