frac{1+sqrt{25}}{sqrt{3}+sqrt{5}}= eching

$$\frac { 1 + \sqrt { 25 } } { \sqrt { 3 } + \sqrt { 5 } } =$$

Baholash

$$3\left(\sqrt{5}-\sqrt{3}\right)\approx 1,51205151$$

Yechim qadamlari

25 ning kvadrat ildizini hisoblab, 5 natijaga ega bo‘ling.

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

6 olish uchun 1 va 5'ni qo'shing.

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

\frac{6}{\sqrt{3}+\sqrt{5}} maxrajini \sqrt{3}-\sqrt{5} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{6\left(\sqrt{3}-\sqrt{5}\right)}{\left(\sqrt{3}+\sqrt{5}\right)\left(\sqrt{3}-\sqrt{5}\right)}$$

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

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

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

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

-2 olish uchun 3 dan 5 ni ayirish.

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

-3\left(\sqrt{3}-\sqrt{5}\right) ni olish uchun 6\left(\sqrt{3}-\sqrt{5}\right) ni -2 ga bo‘ling.

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

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

$$-3\sqrt{3}+3\sqrt{5}$$