Issolvi (sqrt{1/2}-frac{sqrt{3}}{3})*sqrt{24}

$$( \sqrt { \frac { 1 } { 2 } } - \frac { \sqrt { 3 } } { 3 } ) \times \sqrt { 24 }$$

Evalwa

$$2\left(\sqrt{3}-\sqrt{2}\right)\approx 0.63567449$$

Passi Qosra tas-Soluzzjonijiet

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

$$\left(\frac{\sqrt{1}}{\sqrt{2}}-\frac{\sqrt{3}}{3}\right)\sqrt{24}$$

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

$$\left(\frac{1}{\sqrt{2}}-\frac{\sqrt{3}}{3}\right)\sqrt{24}$$

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

$$\left(\frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}-\frac{\sqrt{3}}{3}\right)\sqrt{24}$$

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

$$\left(\frac{\sqrt{2}}{2}-\frac{\sqrt{3}}{3}\right)\sqrt{24}$$

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. L-inqas multiplu komuni ta' 2 u 3 huwa 6. Immultiplika \frac{\sqrt{2}}{2} b'\frac{3}{3}. Immultiplika \frac{\sqrt{3}}{3} b'\frac{2}{2}.

$$\left(\frac{3\sqrt{2}}{6}-\frac{2\sqrt{3}}{6}\right)\sqrt{24}$$

Billi \frac{3\sqrt{2}}{6} u \frac{2\sqrt{3}}{6} għandhom l-istess denominatur, naqqashom billi tnaqqas in-numeraturi tagħhom.

$$\frac{3\sqrt{2}-2\sqrt{3}}{6}\sqrt{24}$$

Iffattura 24=2^{2}\times 6. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{2^{2}\times 6} bħala l-prodott tal-għeruq kwadrati \sqrt{2^{2}}\sqrt{6}. Ħu l-għerq kwadrat ta' 2^{2}.

$$\frac{3\sqrt{2}-2\sqrt{3}}{6}\times 2\sqrt{6}$$

Ikkanċella l-akbar fattur komuni 6 f'2 u 6.

$$\frac{3\sqrt{2}-2\sqrt{3}}{3}\sqrt{6}$$

Esprimi \frac{3\sqrt{2}-2\sqrt{3}}{3}\sqrt{6} bħala frazzjoni waħda.

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

Uża l-propjetà distributtiva biex timmultiplika 3\sqrt{2}-2\sqrt{3} b'\sqrt{6}.

$$\frac{3\sqrt{2}\sqrt{6}-2\sqrt{3}\sqrt{6}}{3}$$

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

$$\frac{3\sqrt{2}\sqrt{2}\sqrt{3}-2\sqrt{3}\sqrt{6}}{3}$$

Immultiplika \sqrt{2} u \sqrt{2} biex tikseb 2.

$$\frac{3\times 2\sqrt{3}-2\sqrt{3}\sqrt{6}}{3}$$

Immultiplika 3 u 2 biex tikseb 6.

$$\frac{6\sqrt{3}-2\sqrt{3}\sqrt{6}}{3}$$

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

$$\frac{6\sqrt{3}-2\sqrt{3}\sqrt{3}\sqrt{2}}{3}$$

Immultiplika \sqrt{3} u \sqrt{3} biex tikseb 3.

$$\frac{6\sqrt{3}-2\times 3\sqrt{2}}{3}$$

Immultiplika -2 u 3 biex tikseb -6.

$$\frac{6\sqrt{3}-6\sqrt{2}}{3}$$

Fattur

$$2 {(\sqrt{3} - \sqrt{2})} = 0.63567449$$