Issolvi sqrt{8}+1/2-2sqrt{1/2}

$$\sqrt { 8 } + \frac { 1 } { 2 } - 2 \sqrt { \frac { 1 } { 2 } }$$

Evalwa

$$\sqrt{2}+\frac{1}{2}\approx 1.914213562$$

Passi tas-Soluzzjonijiet

Iffattura 8=2^{2}\times 2. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{2^{2}\times 2} bħala l-prodott tal-għeruq kwadrati \sqrt{2^{2}}\sqrt{2}. Ħu l-għerq kwadrat ta' 2^{2}.

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

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \sqrt{\frac{1}{2}} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{1}}{\sqrt{2}}.

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

Ikkalkula l-għerq kwadrat ta' 1 u ikseb 1.

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

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

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

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

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

Annulla 2 u 2.

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

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

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

Fattur

$$\frac{2 \sqrt{2} + 1}{2} = 1.9142135623730951$$