Issolvi -5sqrt{8/27}*sqrt{11/4}*(-3sqrt{54})

$$- 5 \sqrt { \frac { 8 } { 27 } } \times \sqrt { 1 \frac { 1 } { 4 } } \times ( - 3 \sqrt { 54 } )$$

Evalwa

$$30\sqrt{5}\approx 67.082039325$$

Passi tas-Soluzzjonijiet

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \sqrt{\frac{8}{27}} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{8}}{\sqrt{27}}.

$$-5\times \frac{\sqrt{8}}{\sqrt{27}}\sqrt{\frac{4+1}{4}}\left(-3\right)\sqrt{54}$$

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}.

$$-5\times \frac{2\sqrt{2}}{\sqrt{27}}\sqrt{\frac{4+1}{4}}\left(-3\right)\sqrt{54}$$

Iffattura 27=3^{2}\times 3. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{3^{2}\times 3} bħala l-prodott tal-għeruq kwadrati \sqrt{3^{2}}\sqrt{3}. Ħu l-għerq kwadrat ta' 3^{2}.

$$-5\times \frac{2\sqrt{2}}{3\sqrt{3}}\sqrt{\frac{4+1}{4}}\left(-3\right)\sqrt{54}$$

Irrazzjonalizza d-denominatur tal-\frac{2\sqrt{2}}{3\sqrt{3}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{3}.

$$-5\times \frac{2\sqrt{2}\sqrt{3}}{3\left(\sqrt{3}\right)^{2}}\sqrt{\frac{4+1}{4}}\left(-3\right)\sqrt{54}$$

Il-kwadrat ta' \sqrt{3} huwa 3.

$$-5\times \frac{2\sqrt{2}\sqrt{3}}{3\times 3}\sqrt{\frac{4+1}{4}}\left(-3\right)\sqrt{54}$$

Biex timmultiplika \sqrt{2} u \sqrt{3}, immultiplika n-numri taħt l-għerq kwadrat.

$$-5\times \frac{2\sqrt{6}}{3\times 3}\sqrt{\frac{4+1}{4}}\left(-3\right)\sqrt{54}$$

Immultiplika 3 u 3 biex tikseb 9.

$$-5\times \frac{2\sqrt{6}}{9}\sqrt{\frac{4+1}{4}}\left(-3\right)\sqrt{54}$$

Żid 4 u 1 biex tikseb 5.

$$-5\times \frac{2\sqrt{6}}{9}\sqrt{\frac{5}{4}}\left(-3\right)\sqrt{54}$$

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \sqrt{\frac{5}{4}} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{5}}{\sqrt{4}}.

$$-5\times \frac{2\sqrt{6}}{9}\times \frac{\sqrt{5}}{\sqrt{4}}\left(-3\right)\sqrt{54}$$

Ikkalkula l-għerq kwadrat ta' 4 u ikseb 2.

$$-5\times \frac{2\sqrt{6}}{9}\times \frac{\sqrt{5}}{2}\left(-3\right)\sqrt{54}$$

Immultiplika -5 u -3 biex tikseb 15.

$$15\times \frac{2\sqrt{6}}{9}\times \frac{\sqrt{5}}{2}\sqrt{54}$$

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}.

$$15\times \frac{2\sqrt{6}}{9}\times \frac{\sqrt{5}}{2}\times 3\sqrt{6}$$

Immultiplika 15 u 3 biex tikseb 45.

$$45\times \frac{2\sqrt{6}}{9}\times \frac{\sqrt{5}}{2}\sqrt{6}$$

Ikkanċella l-akbar fattur komuni 9 f'45 u 9.

$$5\times 2\sqrt{6}\times \frac{\sqrt{5}}{2}\sqrt{6}$$

Esprimi 5\times 2\sqrt{6}\times \frac{\sqrt{5}}{2} bħala frazzjoni waħda.

$$\frac{5\times 2\sqrt{6}\sqrt{5}}{2}\sqrt{6}$$

Annulla 2 u 2.

$$5\sqrt{6}\sqrt{5}\sqrt{6}$$

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

$$5\times 6\sqrt{5}$$

Immultiplika 5 u 6 biex tikseb 30.

$$30\sqrt{5}$$