Issolvi frac{sqrt{66}}{sqrt{54}}

$$\frac { \sqrt { 66 } } { \sqrt { 54 } }$$

Evalwa

$$\frac{\sqrt{11}}{3}\approx 1.105541597$$

Passi tas-Soluzzjonijiet

Iffattura 54=3^{2}\times 6. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{3^{2}\times 6} bħala l-prodott tal-għeruq kwadrati \sqrt{3^{2}}\sqrt{6}. Ħu l-għerq kwadrat ta' 3^{2}.

$$\frac{\sqrt{66}}{3\sqrt{6}}$$

Irrazzjonalizza d-denominatur tal-\frac{\sqrt{66}}{3\sqrt{6}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{6}.

$$\frac{\sqrt{66}\sqrt{6}}{3\left(\sqrt{6}\right)^{2}}$$

Il-kwadrat ta' \sqrt{6} huwa 6.

$$\frac{\sqrt{66}\sqrt{6}}{3\times 6}$$

Iffattura 66=6\times 11. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{6\times 11} bħala l-prodott tal-għeruq kwadrati \sqrt{6}\sqrt{11}.

$$\frac{\sqrt{6}\sqrt{11}\sqrt{6}}{3\times 6}$$

Immultiplika \sqrt{6} u \sqrt{6} biex tikseb 6.

$$\frac{6\sqrt{11}}{3\times 6}$$

Immultiplika 3 u 6 biex tikseb 18.

$$\frac{6\sqrt{11}}{18}$$

Iddividi 6\sqrt{11} b'18 biex tikseb\frac{1}{3}\sqrt{11}.

$$\frac{1}{3}\sqrt{11}$$