Issolvi sqrt{3/4}*(-sqrt{22/3})*sqrt{56}

$$\sqrt { \frac { 3 } { 4 } } \times ( - \sqrt { 2 \frac { 2 } { 3 } } ) \times \sqrt { 56 }$$

Evalwa

$$-4\sqrt{7}\approx -10.583005244$$

Passi tas-Soluzzjonijiet

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \sqrt{\frac{3}{4}} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{3}}{\sqrt{4}}.

$$\frac{\sqrt{3}}{\sqrt{4}}\left(-\sqrt{\frac{2\times 3+2}{3}}\right)\sqrt{56}$$

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

$$\frac{\sqrt{3}}{2}\left(-\sqrt{\frac{2\times 3+2}{3}}\right)\sqrt{56}$$

Immultiplika 2 u 3 biex tikseb 6.

$$\frac{\sqrt{3}}{2}\left(-\sqrt{\frac{6+2}{3}}\right)\sqrt{56}$$

Żid 6 u 2 biex tikseb 8.

$$\frac{\sqrt{3}}{2}\left(-\sqrt{\frac{8}{3}}\right)\sqrt{56}$$

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \sqrt{\frac{8}{3}} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{8}}{\sqrt{3}}.

$$\frac{\sqrt{3}}{2}\left(-\frac{\sqrt{8}}{\sqrt{3}}\right)\sqrt{56}$$

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}.

$$\frac{\sqrt{3}}{2}\left(-\frac{2\sqrt{2}}{\sqrt{3}}\right)\sqrt{56}$$

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

$$\frac{\sqrt{3}}{2}\left(-\frac{2\sqrt{2}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\right)\sqrt{56}$$

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

$$\frac{\sqrt{3}}{2}\left(-\frac{2\sqrt{2}\sqrt{3}}{3}\right)\sqrt{56}$$

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

$$\frac{\sqrt{3}}{2}\left(-\frac{2\sqrt{6}}{3}\right)\sqrt{56}$$

Iffattura 56=2^{2}\times 14. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{2^{2}\times 14} bħala l-prodott tal-għeruq kwadrati \sqrt{2^{2}}\sqrt{14}. Ħu l-għerq kwadrat ta' 2^{2}.

$$\frac{\sqrt{3}}{2}\left(-\frac{2\sqrt{6}}{3}\right)\times 2\sqrt{14}$$

Immultiplika \frac{\sqrt{3}}{2} b'-\frac{2\sqrt{6}}{3} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

$$\frac{-\sqrt{3}\times 2\sqrt{6}}{2\times 3}\times 2\sqrt{14}$$

Annulla 2 fin-numeratur u d-denominatur.

$$\frac{-\sqrt{3}\sqrt{6}}{3}\times 2\sqrt{14}$$

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

$$\frac{-\sqrt{3}\sqrt{6}\times 2}{3}\sqrt{14}$$

Esprimi \frac{-\sqrt{3}\sqrt{6}\times 2}{3}\sqrt{14} bħala frazzjoni waħda.

$$\frac{-\sqrt{3}\sqrt{6}\times 2\sqrt{14}}{3}$$

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}.

$$\frac{-\sqrt{3}\sqrt{3}\sqrt{2}\times 2\sqrt{14}}{3}$$

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

$$\frac{-3\sqrt{2}\times 2\sqrt{14}}{3}$$

Iffattura 14=2\times 7. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{2\times 7} bħala l-prodott tal-għeruq kwadrati \sqrt{2}\sqrt{7}.

$$\frac{-3\sqrt{2}\times 2\sqrt{2}\sqrt{7}}{3}$$

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

$$\frac{-3\times 2\times 2\sqrt{7}}{3}$$

Immultiplika -3 u 2 biex tikseb -6.

$$\frac{-6\times 2\sqrt{7}}{3}$$

Immultiplika -6 u 2 biex tikseb -12.

$$\frac{-12\sqrt{7}}{3}$$

Iddividi -12\sqrt{7} b'3 biex tikseb-4\sqrt{7}.

$$-4\sqrt{7}$$