Issolvi frac{1.6+2sqrt{2}}{0.083-0.024sqrt{2}}

$$\frac{ 1.6+2 \sqrt{ 2 } }{ 0.083-0.024 \sqrt{ 2 } }$$

Evalwa

$$\frac{204400\sqrt{2}+228800}{5737}\approx 90.267605395$$

Passi tas-Soluzzjonijiet

Irrazzjonalizza d-denominatur tal-\frac{1.6+2\sqrt{2}}{0.083-0.024\sqrt{2}} billi timmultiplika in-numeratur u d-denominatur mill-0.083+0.024\sqrt{2}.

$$\frac{\left(1.6+2\sqrt{2}\right)\left(0.083+0.024\sqrt{2}\right)}{\left(0.083-0.024\sqrt{2}\right)\left(0.083+0.024\sqrt{2}\right)}$$

Ikkunsidra li \left(0.083-0.024\sqrt{2}\right)\left(0.083+0.024\sqrt{2}\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}.

$$\frac{\left(1.6+2\sqrt{2}\right)\left(0.083+0.024\sqrt{2}\right)}{0.083^{2}-\left(-0.024\sqrt{2}\right)^{2}}$$

Ikkalkula 0.083 bil-power ta' 2 u tikseb 0.006889.

$$\frac{\left(1.6+2\sqrt{2}\right)\left(0.083+0.024\sqrt{2}\right)}{0.006889-\left(-0.024\sqrt{2}\right)^{2}}$$

Espandi \left(-0.024\sqrt{2}\right)^{2}.

$$\frac{\left(1.6+2\sqrt{2}\right)\left(0.083+0.024\sqrt{2}\right)}{0.006889-\left(-0.024\right)^{2}\left(\sqrt{2}\right)^{2}}$$

Ikkalkula -0.024 bil-power ta' 2 u tikseb 0.000576.

$$\frac{\left(1.6+2\sqrt{2}\right)\left(0.083+0.024\sqrt{2}\right)}{0.006889-0.000576\left(\sqrt{2}\right)^{2}}$$

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

$$\frac{\left(1.6+2\sqrt{2}\right)\left(0.083+0.024\sqrt{2}\right)}{0.006889-0.000576\times 2}$$

Immultiplika 0.000576 u 2 biex tikseb 0.001152.

$$\frac{\left(1.6+2\sqrt{2}\right)\left(0.083+0.024\sqrt{2}\right)}{0.006889-0.001152}$$

Naqqas 0.001152 minn 0.006889 biex tikseb 0.005737.

$$\frac{\left(1.6+2\sqrt{2}\right)\left(0.083+0.024\sqrt{2}\right)}{0.005737}$$

Applika l-propjetà distributtiva billi timmultiplika kull terminu ta' 1.6+2\sqrt{2} b'kull terminu ta' 0.083+0.024\sqrt{2}.

$$\frac{0.1328+0.0384\sqrt{2}+0.166\sqrt{2}+0.048\left(\sqrt{2}\right)^{2}}{0.005737}$$

Ikkombina 0.0384\sqrt{2} u 0.166\sqrt{2} biex tikseb 0.2044\sqrt{2}.

$$\frac{0.1328+0.2044\sqrt{2}+0.048\left(\sqrt{2}\right)^{2}}{0.005737}$$

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

$$\frac{0.1328+0.2044\sqrt{2}+0.048\times 2}{0.005737}$$

Immultiplika 0.048 u 2 biex tikseb 0.096.

$$\frac{0.1328+0.2044\sqrt{2}+0.096}{0.005737}$$

Żid 0.1328 u 0.096 biex tikseb 0.2288.

$$\frac{0.2288+0.2044\sqrt{2}}{0.005737}$$