Issolvi frac{10-sqrt{32}}{sqrt{2}}

$$\frac { 10 - \sqrt { 32 } } { \sqrt { 2 } }$$

Evalwa

$$5\sqrt{2}-4\approx 3.071067812$$

Passi tas-Soluzzjonijiet

Iffattura 32=4^{2}\times 2. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{4^{2}\times 2} bħala l-prodott tal-għeruq kwadrati \sqrt{4^{2}}\sqrt{2}. Ħu l-għerq kwadrat ta' 4^{2}.

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

Irrazzjonalizza d-denominatur tal-\frac{10-4\sqrt{2}}{\sqrt{2}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{2}.

$$\frac{\left(10-4\sqrt{2}\right)\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

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

$$\frac{\left(10-4\sqrt{2}\right)\sqrt{2}}{2}$$

Uża l-propjetà distributtiva biex timmultiplika 10-4\sqrt{2} b'\sqrt{2}.

$$\frac{10\sqrt{2}-4\left(\sqrt{2}\right)^{2}}{2}$$

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

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

Immultiplika -4 u 2 biex tikseb -8.

$$\frac{10\sqrt{2}-8}{2}$$

Iddividi kull terminu ta' 10\sqrt{2}-8 b'2 biex tikseb5\sqrt{2}-4.

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