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

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

Lahuta teguriteks

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

Lahenduse etapid

Arvutage 4 ruutjuur, et saada 2.

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

Kui avaldised pole tehtes \frac{2abc+\sqrt{10}a^{2}b^{3}c^{5}-\sqrt{6}a^{3}b^{2}c^{6}}{\sqrt{2}abc} veel teguriteks lahutatud, tehke seda.

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

Taandage abc nii lugejas kui ka nimetajas.

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

Ratsionaliseerige korrutades lugeja ja \sqrt{2} nimetaja \frac{-\sqrt{6}ba^{2}c^{5}+\sqrt{10}ab^{2}c^{4}+2}{\sqrt{2}} nimetaja.

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

\sqrt{2} ruut on 2.

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

Kasutage distributiivsusomadust, et korrutada -\sqrt{6}ba^{2}c^{5}+\sqrt{10}ab^{2}c^{4}+2 ja \sqrt{2}.

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

Tegurda 6=2\times 3. Kirjutage \sqrt{2\times 3} toote juured, kui see ruut \sqrt{2}\sqrt{3}.

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

Korrutage \sqrt{2} ja \sqrt{2}, et leida 2.

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

Tegurda 10=2\times 5. Kirjutage \sqrt{2\times 5} toote juured, kui see ruut \sqrt{2}\sqrt{5}.

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

Korrutage \sqrt{2} ja \sqrt{2}, et leida 2.

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

Mõelge valemile -2ba^{2}c^{5}\times 3^{\frac{1}{2}}+2ab^{2}c^{4}\times 5^{\frac{1}{2}}+2\times 2^{\frac{1}{2}}. Tooge 2 sulgude ette.

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

Kirjutage ümber täielik teguriteks jaotatud avaldis. Lihtsustage.

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

Arvuta

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