Lahenda frac{(sqrt{6}-sqrt{12})*sqrt{3}}{sqrt{6}}+sqrt{6}

$$\frac { ( \sqrt { 6 } - \sqrt { 12 } ) \times \sqrt { 3 } } { \sqrt { 6 } } + \sqrt { 6 }$$

Arvuta

$$\sqrt{3}\approx 1,732050808$$

Lahenduse etapid

Tegurda 12=2^{2}\times 3. Kirjutage \sqrt{2^{2}\times 3} toote juured, kui see ruut \sqrt{2^{2}}\sqrt{3}. Leidke 2^{2} ruutjuur.

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

Ratsionaliseerige korrutades lugeja ja \sqrt{6} nimetaja \frac{\left(\sqrt{6}-2\sqrt{3}\right)\sqrt{3}}{\sqrt{6}} nimetaja.

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

\sqrt{6} ruut on 6.

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

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

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

Korrutage \sqrt{3} ja \sqrt{3}, et leida 3.

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

Jagage \left(\sqrt{6}-2\sqrt{3}\right)\times 3\sqrt{2} väärtusega 6, et leida \left(\sqrt{6}-2\sqrt{3}\right)\times \frac{1}{2}\sqrt{2}.

$$\left(\sqrt{6}-2\sqrt{3}\right)\times \frac{1}{2}\sqrt{2}+\sqrt{6}$$

Kasutage distributiivsusomadust, et korrutada \sqrt{6}-2\sqrt{3} ja \frac{1}{2}.

$$\left(\sqrt{6}\times \frac{1}{2}-2\sqrt{3}\times \frac{1}{2}\right)\sqrt{2}+\sqrt{6}$$

Korrutage omavahel -2 ja \frac{1}{2}.

$$\left(\sqrt{6}\times \frac{1}{2}-\sqrt{3}\right)\sqrt{2}+\sqrt{6}$$

Kasutage distributiivsusomadust, et korrutada \sqrt{6}\times \frac{1}{2}-\sqrt{3} ja \sqrt{2}.

$$\sqrt{6}\times \frac{1}{2}\sqrt{2}-\sqrt{3}\sqrt{2}+\sqrt{6}$$

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

$$\sqrt{2}\sqrt{3}\times \frac{1}{2}\sqrt{2}-\sqrt{3}\sqrt{2}+\sqrt{6}$$

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

$$2\times \frac{1}{2}\sqrt{3}-\sqrt{3}\sqrt{2}+\sqrt{6}$$

Taandage 2 ja 2.

$$\sqrt{3}-\sqrt{3}\sqrt{2}+\sqrt{6}$$

\sqrt{3} ja \sqrt{2} korrutage numbrid, mis on sama juur.

$$\sqrt{3}-\sqrt{6}+\sqrt{6}$$

Kombineerige -\sqrt{6} ja \sqrt{6}, et leida 0.

$$\sqrt{3}$$