Issolvi 2-frac{3+sqrt{4}-sqrt{2}}{2sqrt{2}}

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

Evalwa

$$-\frac{5\sqrt{2}}{4}+\frac{5}{2}\approx 0.732233047$$

Passi Qosra tas-Soluzzjonijiet

Ikkalkula l-għerq kwadrat ta' 4 u ikseb 2.

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

Żid 3 u 2 biex tikseb 5.

$$2-\frac{5-\sqrt{2}}{2\sqrt{2}}$$

Irrazzjonalizza d-denominatur tal-\frac{5-\sqrt{2}}{2\sqrt{2}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{2}.

$$2-\frac{\left(5-\sqrt{2}\right)\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}$$

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

$$2-\frac{\left(5-\sqrt{2}\right)\sqrt{2}}{2\times 2}$$

Immultiplika 2 u 2 biex tikseb 4.

$$2-\frac{\left(5-\sqrt{2}\right)\sqrt{2}}{4}$$

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. Immultiplika 2 b'\frac{4}{4}.

$$\frac{2\times 4}{4}-\frac{\left(5-\sqrt{2}\right)\sqrt{2}}{4}$$

Billi \frac{2\times 4}{4} u \frac{\left(5-\sqrt{2}\right)\sqrt{2}}{4} għandhom l-istess denominatur, naqqashom billi tnaqqas in-numeraturi tagħhom.

$$\frac{2\times 4-\left(5-\sqrt{2}\right)\sqrt{2}}{4}$$

Agħmel il-multiplikazzjonijiet fi 2\times 4-\left(5-\sqrt{2}\right)\sqrt{2}.

$$\frac{8-5\sqrt{2}+2}{4}$$

Agħmel il-kalkoli fi 8-5\sqrt{2}+2.

$$\frac{10-5\sqrt{2}}{4}$$

Fattur

$$\frac{5 \sqrt{2} {(\sqrt{2} - 1)}}{4} = 0.7322330470336313$$