frac{sqrt{4}abc+sqrt{10}a^{2}b^{3}c^5-sqrt{6}a^3b^2c^6}{sqrt{2}abc} eching

$$\frac { \sqrt { 4 } a b c + \sqrt { 10 } a ^ { 2 } b ^ { 3 } c ^ { 5 } - \sqrt { 6 } a ^ { 3 } b ^ { 2 } c ^ { 6 } } { \sqrt { 2 } a b c }$$

Omil

$$\frac{\sqrt{2}\left(-\sqrt{6}ba^{2}c^{5}+\sqrt{10}ab^{2}c^{4}+2\right)}{2}$$

Yechim qadamlari

4 ning kvadrat ildizini hisoblab, 2 natijaga ega bo‘ling.

$$factor(\frac{2abc+\sqrt{10}a^{2}b^{3}c^{5}-\sqrt{6}a^{3}b^{2}c^{6}}{\sqrt{2}abc})$$

\frac{2abc+\sqrt{10}a^{2}b^{3}c^{5}-\sqrt{6}a^{3}b^{2}c^{6}}{\sqrt{2}abc} ichida hali faktorlanmagan ifodalarni faktorlang.

$$factor(\frac{abc\left(-\sqrt{6}ba^{2}c^{5}+\sqrt{10}ab^{2}c^{4}+2\right)}{\sqrt{2}abc})$$

Surat va maxrajdagi ikkala abc ni qisqartiring.

$$factor(\frac{-\sqrt{6}ba^{2}c^{5}+\sqrt{10}ab^{2}c^{4}+2}{\sqrt{2}})$$

\frac{-\sqrt{6}ba^{2}c^{5}+\sqrt{10}ab^{2}c^{4}+2}{\sqrt{2}} maxrajini \sqrt{2} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$factor(\frac{\left(-\sqrt{6}ba^{2}c^{5}+\sqrt{10}ab^{2}c^{4}+2\right)\sqrt{2}}{\left(\sqrt{2}\right)^{2}})$$

\sqrt{2} kvadrati – 2.

$$factor(\frac{\left(-\sqrt{6}ba^{2}c^{5}+\sqrt{10}ab^{2}c^{4}+2\right)\sqrt{2}}{2})$$

-\sqrt{6}ba^{2}c^{5}+\sqrt{10}ab^{2}c^{4}+2 ga \sqrt{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$factor(\frac{-\sqrt{6}ba^{2}c^{5}\sqrt{2}+\sqrt{10}ab^{2}c^{4}\sqrt{2}+2\sqrt{2}}{2})$$

Faktor: 6=2\times 3. \sqrt{2\times 3} koʻpaytmasining kvadrat ildizini \sqrt{2}\sqrt{3} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing.

$$factor(\frac{-\sqrt{2}\sqrt{3}ba^{2}c^{5}\sqrt{2}+\sqrt{10}ab^{2}c^{4}\sqrt{2}+2\sqrt{2}}{2})$$

2 hosil qilish uchun \sqrt{2} va \sqrt{2} ni ko'paytirish.

$$factor(\frac{-2ba^{2}c^{5}\sqrt{3}+\sqrt{10}ab^{2}c^{4}\sqrt{2}+2\sqrt{2}}{2})$$

Faktor: 10=2\times 5. \sqrt{2\times 5} koʻpaytmasining kvadrat ildizini \sqrt{2}\sqrt{5} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing.

$$factor(\frac{-2ba^{2}c^{5}\sqrt{3}+\sqrt{2}\sqrt{5}ab^{2}c^{4}\sqrt{2}+2\sqrt{2}}{2})$$

2 hosil qilish uchun \sqrt{2} va \sqrt{2} ni ko'paytirish.

$$factor(\frac{-2ba^{2}c^{5}\sqrt{3}+2ab^{2}c^{4}\sqrt{5}+2\sqrt{2}}{2})$$

Hisoblang: -2ba^{2}c^{5}\times 3^{\frac{1}{2}}+2ab^{2}c^{4}\times 5^{\frac{1}{2}}+2\times 2^{\frac{1}{2}}. 2 omili.

$$2\left(-ba^{2}c^{5}\sqrt{3}+ab^{2}c^{4}\sqrt{5}+\sqrt{2}\right)$$

Toʻliq ajratilgan ifodani qaytadan yozing. Qisqartirish.

$$-ba^{2}c^{5}\sqrt{3}+ab^{2}c^{4}\sqrt{5}+\sqrt{2}$$

Baholash

$$-\frac{2\sqrt{3}ba^{2}c^{5}}{2}+\frac{2\sqrt{5}ab^{2}c^{4}}{2}+\sqrt{2}$$