Issolvi frac{2sqrt{18}-sqrt{32}}{sqrt{8}+sqrt{2}}

$$\frac { 2 \sqrt { 18 } - \sqrt { 32 } } { \sqrt { 8 } + \sqrt { 2 } }$$

Evalwa

$$\frac{2}{3}\approx 0.666666667$$

Passi tas-Soluzzjonijiet

Iffattura 18=3^{2}\times 2. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{3^{2}\times 2} bħala l-prodott tal-għeruq kwadrati \sqrt{3^{2}}\sqrt{2}. Ħu l-għerq kwadrat ta' 3^{2}.

$$\frac{2\times 3\sqrt{2}-\sqrt{32}}{\sqrt{8}+\sqrt{2}}$$

Immultiplika 2 u 3 biex tikseb 6.

$$\frac{6\sqrt{2}-\sqrt{32}}{\sqrt{8}+\sqrt{2}}$$

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}.

$$\frac{6\sqrt{2}-4\sqrt{2}}{\sqrt{8}+\sqrt{2}}$$

Ikkombina 6\sqrt{2} u -4\sqrt{2} biex tikseb 2\sqrt{2}.

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

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}.

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

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

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

Annulla \sqrt{2} fin-numeratur u d-denominatur.

$$\frac{2}{3}$$

Fattur

$$\frac{2}{3} = 0.6666666666666666$$