Réitigh (frac{sqrt{2}}{sqrt{2}-18})^2

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

Luacháil

$$\frac{18\sqrt{2}+163}{25921}\approx 0.007270393$$

Céimeanna Réitigh

Iolraigh an t-uimhreoir agus an t-ainmneoir faoi \sqrt{2}+18 chun ainmneoir \frac{\sqrt{2}}{\sqrt{2}-18} a thiontú in uimhir chóimheasta.

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

Mar shampla \left(\sqrt{2}-18\right)\left(\sqrt{2}+18\right). Is féidir iolrúchán a athrú ó bhonn go dtí difríocht na gcearnóg ag úsáid na rialach seo: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Cearnóg \sqrt{2}. Cearnóg 18.

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

Dealaigh 324 ó 2 chun -322 a fháil.

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

Chun \frac{\sqrt{2}\left(\sqrt{2}+18\right)}{-322} a iolrú i gcumhacht, iolraigh an t-uimhreoir agus an t-ainmneoir araon i gcumhacht agus déan iad a roinnt ansin.

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

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

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

Is é 2 uimhir chearnach \sqrt{2}.

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

Úsáid an teoirim dhéthéarmach \left(a+b\right)^{2}=a^{2}+2ab+b^{2} chun \left(\sqrt{2}+18\right)^{2} a leathnú.

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

Is é 2 uimhir chearnach \sqrt{2}.

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

Suimigh 2 agus 324 chun 326 a fháil.

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

Ríomh cumhacht -322 de 2 agus faigh 103684.

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

Roinn 2\left(326+36\sqrt{2}\right) faoi 103684 chun \frac{1}{51842}\left(326+36\sqrt{2}\right) a fháil.

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

Úsáid an t-airí dáileach chun \frac{1}{51842} a mhéadú faoi 326+36\sqrt{2}.

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

Fairsingigh

$$\frac{18 \sqrt{2} + 163}{25921} = 0.007270392505023561$$

Céimeanna Réitigh

Iolraigh an t-uimhreoir agus an t-ainmneoir faoi \sqrt{2}+18 chun ainmneoir \frac{\sqrt{2}}{\sqrt{2}-18} a thiontú in uimhir chóimheasta.

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

Mar shampla \left(\sqrt{2}-18\right)\left(\sqrt{2}+18\right). Is féidir iolrúchán a athrú ó bhonn go dtí difríocht na gcearnóg ag úsáid na rialach seo: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Cearnóg \sqrt{2}. Cearnóg 18.

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

Dealaigh 324 ó 2 chun -322 a fháil.

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

Chun \frac{\sqrt{2}\left(\sqrt{2}+18\right)}{-322} a iolrú i gcumhacht, iolraigh an t-uimhreoir agus an t-ainmneoir araon i gcumhacht agus déan iad a roinnt ansin.

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

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

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

Is é 2 uimhir chearnach \sqrt{2}.

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

Úsáid an teoirim dhéthéarmach \left(a+b\right)^{2}=a^{2}+2ab+b^{2} chun \left(\sqrt{2}+18\right)^{2} a leathnú.

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

Is é 2 uimhir chearnach \sqrt{2}.

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

Suimigh 2 agus 324 chun 326 a fháil.

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

Ríomh cumhacht -322 de 2 agus faigh 103684.

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

Roinn 2\left(326+36\sqrt{2}\right) faoi 103684 chun \frac{1}{51842}\left(326+36\sqrt{2}\right) a fháil.

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

Úsáid an t-airí dáileach chun \frac{1}{51842} a mhéadú faoi 326+36\sqrt{2}.

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