frac{sqrt{35}-sqrt{21}}{sqrt{7}} eching

$$\frac { \sqrt { 35 } - \sqrt { 21 } } { \sqrt { 7 } }$$

Baholash

$$\sqrt{5}-\sqrt{3}\approx 0,50401717$$

Yechim qadamlari

\frac{\sqrt{35}-\sqrt{21}}{\sqrt{7}} maxrajini \sqrt{7} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{\left(\sqrt{35}-\sqrt{21}\right)\sqrt{7}}{\left(\sqrt{7}\right)^{2}}$$

\sqrt{7} kvadrati – 7.

$$\frac{\left(\sqrt{35}-\sqrt{21}\right)\sqrt{7}}{7}$$

\sqrt{35}-\sqrt{21} ga \sqrt{7} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{\sqrt{35}\sqrt{7}-\sqrt{21}\sqrt{7}}{7}$$

Faktor: 35=7\times 5. \sqrt{7\times 5} koʻpaytmasining kvadrat ildizini \sqrt{7}\sqrt{5} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing.

$$\frac{\sqrt{7}\sqrt{5}\sqrt{7}-\sqrt{21}\sqrt{7}}{7}$$

7 hosil qilish uchun \sqrt{7} va \sqrt{7} ni ko'paytirish.

$$\frac{7\sqrt{5}-\sqrt{21}\sqrt{7}}{7}$$

Faktor: 21=7\times 3. \sqrt{7\times 3} koʻpaytmasining kvadrat ildizini \sqrt{7}\sqrt{3} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing.

$$\frac{7\sqrt{5}-\sqrt{7}\sqrt{3}\sqrt{7}}{7}$$

7 hosil qilish uchun \sqrt{7} va \sqrt{7} ni ko'paytirish.

$$\frac{7\sqrt{5}-7\sqrt{3}}{7}$$

\sqrt{5}-\sqrt{3} natijani olish uchun 7\sqrt{5}-7\sqrt{3} ning har bir ifodasini 7 ga bo‘ling.

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