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

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

Baholash

$$\frac{\sqrt{5}\left(\sqrt{15}-3\right)}{2}\approx 0,976025053$$

Yechim qadamlari

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

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

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

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

\sqrt{5} kvadratini chiqarish. \sqrt{3} kvadratini chiqarish.

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

2 olish uchun 5 dan 3 ni ayirish.

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

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

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

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

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

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

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

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

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

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

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