Issolvi frac{sqrt{18}}{5sqrt{18}+3sqrt{72}-2sqrt{162}}

$$\frac { \sqrt { 18 } } { 5 \sqrt { 18 } + 3 \sqrt { 72 } - 2 \sqrt { 162 } }$$

Evalwa

$$\frac{1}{5}=0.2$$

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}.

$$\frac{3\sqrt{2}}{5\sqrt{18}+3\sqrt{72}-2\sqrt{162}}$$

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}.

$$\frac{3\sqrt{2}}{5\times 3\sqrt{2}+3\sqrt{72}-2\sqrt{162}}$$

Immultiplika 5 u 3 biex tikseb 15.

$$\frac{3\sqrt{2}}{15\sqrt{2}+3\sqrt{72}-2\sqrt{162}}$$

Iffattura 72=6^{2}\times 2. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{6^{2}\times 2} bħala l-prodott tal-għeruq kwadrati \sqrt{6^{2}}\sqrt{2}. Ħu l-għerq kwadrat ta' 6^{2}.

$$\frac{3\sqrt{2}}{15\sqrt{2}+3\times 6\sqrt{2}-2\sqrt{162}}$$

Immultiplika 3 u 6 biex tikseb 18.

$$\frac{3\sqrt{2}}{15\sqrt{2}+18\sqrt{2}-2\sqrt{162}}$$

Ikkombina 15\sqrt{2} u 18\sqrt{2} biex tikseb 33\sqrt{2}.

$$\frac{3\sqrt{2}}{33\sqrt{2}-2\sqrt{162}}$$

Iffattura 162=9^{2}\times 2. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{9^{2}\times 2} bħala l-prodott tal-għeruq kwadrati \sqrt{9^{2}}\sqrt{2}. Ħu l-għerq kwadrat ta' 9^{2}.

$$\frac{3\sqrt{2}}{33\sqrt{2}-2\times 9\sqrt{2}}$$

Immultiplika -2 u 9 biex tikseb -18.

$$\frac{3\sqrt{2}}{33\sqrt{2}-18\sqrt{2}}$$

Ikkombina 33\sqrt{2} u -18\sqrt{2} biex tikseb 15\sqrt{2}.

$$\frac{3\sqrt{2}}{15\sqrt{2}}$$

Annulla 3\sqrt{2} fin-numeratur u d-denominatur.

$$\frac{1}{5}$$

Fattur

$$\frac{1}{5} = 0.2$$