Lahenda (frac{sqrt{2}}{sqrt{2}-18})^2

$$( \frac { \sqrt { 2 } } { \sqrt { 2 } - 18 } ) ^ { 2 }$$

Arvuta

$$\frac{18\sqrt{2}+163}{25921}\approx 0,007270393$$

Lahenduse etapid

Ratsionaliseerige korrutades lugeja ja \sqrt{2}+18 nimetaja \frac{\sqrt{2}}{\sqrt{2}-18} nimetaja.

$$\left(\frac{\sqrt{2}\left(\sqrt{2}+18\right)}{\left(\sqrt{2}-18\right)\left(\sqrt{2}+18\right)}\right)^{2}$$

Mõelge valemile \left(\sqrt{2}-18\right)\left(\sqrt{2}+18\right). Korrutustehte saab ruutude vaheks teisendada järgmise reegli abil: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\left(\frac{\sqrt{2}\left(\sqrt{2}+18\right)}{\left(\sqrt{2}\right)^{2}-18^{2}}\right)^{2}$$

Tõstke \sqrt{2} ruutu. Tõstke 18 ruutu.

$$\left(\frac{\sqrt{2}\left(\sqrt{2}+18\right)}{2-324}\right)^{2}$$

Lahutage 324 väärtusest 2, et leida -322.

$$\left(\frac{\sqrt{2}\left(\sqrt{2}+18\right)}{-322}\right)^{2}$$

Avaldise \frac{\sqrt{2}\left(\sqrt{2}+18\right)}{-322} astendamiseks astendage nii lugeja kui ka nimetaja ning seejärel tehke jagamistehe.

$$\frac{\left(\sqrt{2}\left(\sqrt{2}+18\right)\right)^{2}}{\left(-322\right)^{2}}$$

Laiendage \left(\sqrt{2}\left(\sqrt{2}+18\right)\right)^{2}.

$$\frac{\left(\sqrt{2}\right)^{2}\left(\sqrt{2}+18\right)^{2}}{\left(-322\right)^{2}}$$

\sqrt{2} ruut on 2.

$$\frac{2\left(\sqrt{2}+18\right)^{2}}{\left(-322\right)^{2}}$$

Kasutage kaksliikme \left(\sqrt{2}+18\right)^{2} arendamiseks binoomvalemit \left(a+b\right)^{2}=a^{2}+2ab+b^{2}.

$$\frac{2\left(\left(\sqrt{2}\right)^{2}+36\sqrt{2}+324\right)}{\left(-322\right)^{2}}$$

\sqrt{2} ruut on 2.

$$\frac{2\left(2+36\sqrt{2}+324\right)}{\left(-322\right)^{2}}$$

Liitke 2 ja 324, et leida 326.

$$\frac{2\left(326+36\sqrt{2}\right)}{\left(-322\right)^{2}}$$

Arvutage 2 aste -322 ja leidke 103684.

$$\frac{2\left(326+36\sqrt{2}\right)}{103684}$$

Jagage 2\left(326+36\sqrt{2}\right) väärtusega 103684, et leida \frac{1}{51842}\left(326+36\sqrt{2}\right).

$$\frac{1}{51842}\left(326+36\sqrt{2}\right)$$

Kasutage distributiivsusomadust, et korrutada \frac{1}{51842} ja 326+36\sqrt{2}.

$$\frac{163}{25921}+\frac{18}{25921}\sqrt{2}$$

Laienda

$$\frac{18 \sqrt{2} + 163}{25921} = 0,007270392505023561$$

Lahenduse etapid

Ratsionaliseerige korrutades lugeja ja \sqrt{2}+18 nimetaja \frac{\sqrt{2}}{\sqrt{2}-18} nimetaja.

$$\left(\frac{\sqrt{2}\left(\sqrt{2}+18\right)}{\left(\sqrt{2}-18\right)\left(\sqrt{2}+18\right)}\right)^{2}$$

Mõelge valemile \left(\sqrt{2}-18\right)\left(\sqrt{2}+18\right). Korrutustehte saab ruutude vaheks teisendada järgmise reegli abil: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\left(\frac{\sqrt{2}\left(\sqrt{2}+18\right)}{\left(\sqrt{2}\right)^{2}-18^{2}}\right)^{2}$$

Tõstke \sqrt{2} ruutu. Tõstke 18 ruutu.

$$\left(\frac{\sqrt{2}\left(\sqrt{2}+18\right)}{2-324}\right)^{2}$$

Lahutage 324 väärtusest 2, et leida -322.

$$\left(\frac{\sqrt{2}\left(\sqrt{2}+18\right)}{-322}\right)^{2}$$

Avaldise \frac{\sqrt{2}\left(\sqrt{2}+18\right)}{-322} astendamiseks astendage nii lugeja kui ka nimetaja ning seejärel tehke jagamistehe.

$$\frac{\left(\sqrt{2}\left(\sqrt{2}+18\right)\right)^{2}}{\left(-322\right)^{2}}$$

Laiendage \left(\sqrt{2}\left(\sqrt{2}+18\right)\right)^{2}.

$$\frac{\left(\sqrt{2}\right)^{2}\left(\sqrt{2}+18\right)^{2}}{\left(-322\right)^{2}}$$

\sqrt{2} ruut on 2.

$$\frac{2\left(\sqrt{2}+18\right)^{2}}{\left(-322\right)^{2}}$$

Kasutage kaksliikme \left(\sqrt{2}+18\right)^{2} arendamiseks binoomvalemit \left(a+b\right)^{2}=a^{2}+2ab+b^{2}.

$$\frac{2\left(\left(\sqrt{2}\right)^{2}+36\sqrt{2}+324\right)}{\left(-322\right)^{2}}$$

\sqrt{2} ruut on 2.

$$\frac{2\left(2+36\sqrt{2}+324\right)}{\left(-322\right)^{2}}$$

Liitke 2 ja 324, et leida 326.

$$\frac{2\left(326+36\sqrt{2}\right)}{\left(-322\right)^{2}}$$

Arvutage 2 aste -322 ja leidke 103684.

$$\frac{2\left(326+36\sqrt{2}\right)}{103684}$$

Jagage 2\left(326+36\sqrt{2}\right) väärtusega 103684, et leida \frac{1}{51842}\left(326+36\sqrt{2}\right).

$$\frac{1}{51842}\left(326+36\sqrt{2}\right)$$

Kasutage distributiivsusomadust, et korrutada \frac{1}{51842} ja 326+36\sqrt{2}.

$$\frac{163}{25921}+\frac{18}{25921}\sqrt{2}$$