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

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

Fachtóirigh

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

Céimeanna Réitigh

Áirigh fréamh chearnach 4 agus faigh 2.

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

Fachtóirigh na sloinn nach bhfuil fachtóirithe cheana in \frac{2abc+\sqrt{10}a^{2}b^{3}c^{5}-\sqrt{6}a^{3}b^{2}c^{6}}{\sqrt{2}abc}.

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

Cealaigh abc mar uimhreoir agus ainmneoir.

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

Iolraigh an t-uimhreoir agus an t-ainmneoir faoi \sqrt{2} chun ainmneoir \frac{-\sqrt{6}ba^{2}c^{5}+\sqrt{10}ab^{2}c^{4}+2}{\sqrt{2}} a thiontú in uimhir chóimheasta.

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

Is é 2 uimhir chearnach \sqrt{2}.

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

Úsáid an t-airí dáileach chun -\sqrt{6}ba^{2}c^{5}+\sqrt{10}ab^{2}c^{4}+2 a mhéadú faoi \sqrt{2}.

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

Fachtóirigh 6=2\times 3. Athscríobh fréamh cearnach an toraidh \sqrt{2\times 3} mar thoradh na bhfréamhacha cearnacha \sqrt{2}\sqrt{3}.

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

Méadaigh \sqrt{2} agus \sqrt{2} chun 2 a fháil.

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

Fachtóirigh 10=2\times 5. Athscríobh fréamh cearnach an toraidh \sqrt{2\times 5} mar thoradh na bhfréamhacha cearnacha \sqrt{2}\sqrt{5}.

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

Méadaigh \sqrt{2} agus \sqrt{2} chun 2 a fháil.

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

Mar shampla -2ba^{2}c^{5}\times 3^{\frac{1}{2}}+2ab^{2}c^{4}\times 5^{\frac{1}{2}}+2\times 2^{\frac{1}{2}}. Fág 2 as an áireamh.

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

Athscríobh an slonn iomlán fachtóirithe. Simpligh.

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

Luacháil

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