Issolvi frac{2-sqrt{2}}{1+sqrt{2}}=

$$\frac { 2 - \sqrt { 2 } } { 1 + \sqrt { 2 } } =$$

Evalwa

$$3\sqrt{2}-4\approx 0.242640687$$

Passi tas-Soluzzjonijiet

Irrazzjonalizza d-denominatur tal-\frac{2-\sqrt{2}}{1+\sqrt{2}} billi timmultiplika in-numeratur u d-denominatur mill-1-\sqrt{2}.

$$\frac{\left(2-\sqrt{2}\right)\left(1-\sqrt{2}\right)}{\left(1+\sqrt{2}\right)\left(1-\sqrt{2}\right)}$$

Ikkunsidra li \left(1+\sqrt{2}\right)\left(1-\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}.

$$\frac{\left(2-\sqrt{2}\right)\left(1-\sqrt{2}\right)}{1^{2}-\left(\sqrt{2}\right)^{2}}$$

Ikkwadra 1. Ikkwadra \sqrt{2}.

$$\frac{\left(2-\sqrt{2}\right)\left(1-\sqrt{2}\right)}{1-2}$$

Naqqas 2 minn 1 biex tikseb -1.

$$\frac{\left(2-\sqrt{2}\right)\left(1-\sqrt{2}\right)}{-1}$$

Kwalunkwe ħaġa diviża b '-1 jagħtik oppost tiegħu.

$$-\left(2-\sqrt{2}\right)\left(1-\sqrt{2}\right)$$

Applika l-propjetà distributtiva billi timmultiplika kull terminu ta' 2-\sqrt{2} b'kull terminu ta' 1-\sqrt{2}.

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

Ikkombina -2\sqrt{2} u -\sqrt{2} biex tikseb -3\sqrt{2}.

$$-\left(2-3\sqrt{2}+\left(\sqrt{2}\right)^{2}\right)$$

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

$$-\left(2-3\sqrt{2}+2\right)$$

Żid 2 u 2 biex tikseb 4.

$$-\left(4-3\sqrt{2}\right)$$

Biex issib l-oppost ta' 4-3\sqrt{2}, sib l-oppost ta' kull terminu.

$$-4-\left(-3\sqrt{2}\right)$$

L-oppost ta' -3\sqrt{2} huwa 3\sqrt{2}.

$$-4+3\sqrt{2}$$

Fattur

$$3 \sqrt{2} - 4 = 0.242640687$$