Issolvi frac{20^2+{left(20sqrt{2}right)}^2-400}{2*20*20sqrt{2}}

$$\frac{ { 20 }^{ 2 } + { \left(20 \sqrt{ 2 } \right) }^{ 2 } -400 }{ 2 \times 20 \times 20 \sqrt{ 2 } }$$

Evalwa

$$\frac{\sqrt{2}}{2}\approx 0.707106781$$

Passi tas-Soluzzjonijiet

Ikkalkula 20 bil-power ta' 2 u tikseb 400.

$$\frac{400+\left(20\sqrt{2}\right)^{2}-400}{2\times 20\times 20\sqrt{2}}$$

Espandi \left(20\sqrt{2}\right)^{2}.

$$\frac{400+20^{2}\left(\sqrt{2}\right)^{2}-400}{2\times 20\times 20\sqrt{2}}$$

Ikkalkula 20 bil-power ta' 2 u tikseb 400.

$$\frac{400+400\left(\sqrt{2}\right)^{2}-400}{2\times 20\times 20\sqrt{2}}$$

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

$$\frac{400+400\times 2-400}{2\times 20\times 20\sqrt{2}}$$

Immultiplika 400 u 2 biex tikseb 800.

$$\frac{400+800-400}{2\times 20\times 20\sqrt{2}}$$

Żid 400 u 800 biex tikseb 1200.

$$\frac{1200-400}{2\times 20\times 20\sqrt{2}}$$

Naqqas 400 minn 1200 biex tikseb 800.

$$\frac{800}{2\times 20\times 20\sqrt{2}}$$

Immultiplika 2 u 20 biex tikseb 40.

$$\frac{800}{40\times 20\sqrt{2}}$$

Immultiplika 40 u 20 biex tikseb 800.

$$\frac{800}{800\sqrt{2}}$$

Irrazzjonalizza d-denominatur tal-\frac{800}{800\sqrt{2}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{2}.

$$\frac{800\sqrt{2}}{800\left(\sqrt{2}\right)^{2}}$$

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

$$\frac{800\sqrt{2}}{800\times 2}$$

Annulla 800 fin-numeratur u d-denominatur.

$$\frac{\sqrt{2}}{2}$$