Lahenda frac{2sqrt{2}}{5-2sqrt{6}}

$$\frac{ 2 \sqrt{ 2 } }{ 5-2 \sqrt{ 6 } }$$

Arvuta

$$8\sqrt{3}+10\sqrt{2}\approx 27,998542084$$

Lahenduse etapid

Ratsionaliseerige korrutades lugeja ja 5+2\sqrt{6} nimetaja \frac{2\sqrt{2}}{5-2\sqrt{6}} nimetaja.

$$\frac{2\sqrt{2}\left(5+2\sqrt{6}\right)}{\left(5-2\sqrt{6}\right)\left(5+2\sqrt{6}\right)}$$

Mõelge valemile \left(5-2\sqrt{6}\right)\left(5+2\sqrt{6}\right). Korrutustehte saab ruutude vaheks teisendada järgmise reegli abil: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{2\sqrt{2}\left(5+2\sqrt{6}\right)}{5^{2}-\left(-2\sqrt{6}\right)^{2}}$$

Arvutage 2 aste 5 ja leidke 25.

$$\frac{2\sqrt{2}\left(5+2\sqrt{6}\right)}{25-\left(-2\sqrt{6}\right)^{2}}$$

Laiendage \left(-2\sqrt{6}\right)^{2}.

$$\frac{2\sqrt{2}\left(5+2\sqrt{6}\right)}{25-\left(-2\right)^{2}\left(\sqrt{6}\right)^{2}}$$

Arvutage 2 aste -2 ja leidke 4.

$$\frac{2\sqrt{2}\left(5+2\sqrt{6}\right)}{25-4\left(\sqrt{6}\right)^{2}}$$

\sqrt{6} ruut on 6.

$$\frac{2\sqrt{2}\left(5+2\sqrt{6}\right)}{25-4\times 6}$$

Korrutage 4 ja 6, et leida 24.

$$\frac{2\sqrt{2}\left(5+2\sqrt{6}\right)}{25-24}$$

Lahutage 24 väärtusest 25, et leida 1.

$$\frac{2\sqrt{2}\left(5+2\sqrt{6}\right)}{1}$$

Arv jagatuna ühega annab tulemiks arvu enda.

$$2\sqrt{2}\left(5+2\sqrt{6}\right)$$

Kasutage distributiivsusomadust, et korrutada 2\sqrt{2} ja 5+2\sqrt{6}.

$$10\sqrt{2}+4\sqrt{2}\sqrt{6}$$

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

$$10\sqrt{2}+4\sqrt{2}\sqrt{2}\sqrt{3}$$

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

$$10\sqrt{2}+4\times 2\sqrt{3}$$

Korrutage 4 ja 2, et leida 8.

$$10\sqrt{2}+8\sqrt{3}$$