Lahenda 5/sqrt{6-sqrt{8}}

$$\frac{ 5 }{ \sqrt{ 6 } - \sqrt{ 8 } }$$

Arvuta

$$-\frac{5\sqrt{6}}{2}-5\sqrt{2}\approx -13,194792169$$

Lahenduse etapid

Tegurda 8=2^{2}\times 2. Kirjutage \sqrt{2^{2}\times 2} toote juured, kui see ruut \sqrt{2^{2}}\sqrt{2}. Leidke 2^{2} ruutjuur.

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

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

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

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

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

\sqrt{6} ruut on 6.

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

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

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

Arvutage 2 aste -2 ja leidke 4.

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

\sqrt{2} ruut on 2.

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

Korrutage 4 ja 2, et leida 8.

$$\frac{5\left(\sqrt{6}+2\sqrt{2}\right)}{6-8}$$

Lahutage 8 väärtusest 6, et leida -2.

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

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

$$\frac{5\sqrt{6}+10\sqrt{2}}{-2}$$