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

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

Evalwa

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

Passi tas-Soluzzjonijiet

Irrazzjonalizza d-denominatur tal-\frac{\sqrt{2}}{\sqrt{2}-18} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{2}+18.

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

Ikkunsidra li \left(\sqrt{2}-18\right)\left(\sqrt{2}+18\right). Il-multiplikazzjoni tista' tiġi ttrasformata fid-differenza tal-kwadrati li jużaw ir-regola: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Ikkwadra \sqrt{2}. Ikkwadra 18.

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

Naqqas 324 minn 2 biex tikseb -322.

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

Biex tgħolli \frac{\sqrt{2}\left(\sqrt{2}+18\right)}{-322} għal qawwa, għolli kemm in-numeratur u d-denominatur għall-qawwa u mbagħad iddividi.

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

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

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

Il-kwadrat ta' \sqrt{2} huwa 2.

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

Uża teorema binomjali \left(a+b\right)^{2}=a^{2}+2ab+b^{2} biex tespandi \left(\sqrt{2}+18\right)^{2}.

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

Il-kwadrat ta' \sqrt{2} huwa 2.

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

Żid 2 u 324 biex tikseb 326.

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

Ikkalkula -322 bil-power ta' 2 u tikseb 103684.

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

Iddividi 2\left(326+36\sqrt{2}\right) b'103684 biex tikseb\frac{1}{51842}\left(326+36\sqrt{2}\right).

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

Uża l-propjetà distributtiva biex timmultiplika \frac{1}{51842} b'326+36\sqrt{2}.

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

Espandi

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

Passi tas-Soluzzjonijiet

Irrazzjonalizza d-denominatur tal-\frac{\sqrt{2}}{\sqrt{2}-18} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{2}+18.

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

Ikkunsidra li \left(\sqrt{2}-18\right)\left(\sqrt{2}+18\right). Il-multiplikazzjoni tista' tiġi ttrasformata fid-differenza tal-kwadrati li jużaw ir-regola: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Ikkwadra \sqrt{2}. Ikkwadra 18.

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

Naqqas 324 minn 2 biex tikseb -322.

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

Biex tgħolli \frac{\sqrt{2}\left(\sqrt{2}+18\right)}{-322} għal qawwa, għolli kemm in-numeratur u d-denominatur għall-qawwa u mbagħad iddividi.

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

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

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

Il-kwadrat ta' \sqrt{2} huwa 2.

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

Uża teorema binomjali \left(a+b\right)^{2}=a^{2}+2ab+b^{2} biex tespandi \left(\sqrt{2}+18\right)^{2}.

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

Il-kwadrat ta' \sqrt{2} huwa 2.

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

Żid 2 u 324 biex tikseb 326.

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

Ikkalkula -322 bil-power ta' 2 u tikseb 103684.

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

Iddividi 2\left(326+36\sqrt{2}\right) b'103684 biex tikseb\frac{1}{51842}\left(326+36\sqrt{2}\right).

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

Uża l-propjetà distributtiva biex timmultiplika \frac{1}{51842} b'326+36\sqrt{2}.

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