Issolvi 3sqrt{22/3}div2sqrt{2/5}*(-1/8sqrt{15})

$$3 \sqrt { 2 \frac { 2 } { 3 } } \div 2 \sqrt { \frac { 2 } { 5 } } \times ( - \frac { 1 } { 8 } \sqrt { 15 } )$$

Evalwa

$$-\frac{3}{4}=-0.75$$

Passi tas-Soluzzjonijiet

Immultiplika 2 u 3 biex tikseb 6.

$$\frac{3\sqrt{\frac{6+2}{3}}}{2}\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

Żid 6 u 2 biex tikseb 8.

$$\frac{3\sqrt{\frac{8}{3}}}{2}\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

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

$$\frac{3\times \frac{\sqrt{8}}{\sqrt{3}}}{2}\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

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}.

$$\frac{3\times \frac{2\sqrt{2}}{\sqrt{3}}}{2}\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

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

$$\frac{3\times \frac{2\sqrt{2}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}}{2}\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

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

$$\frac{3\times \frac{2\sqrt{2}\sqrt{3}}{3}}{2}\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

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

$$\frac{3\times \frac{2\sqrt{6}}{3}}{2}\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

Annulla 3 u 3.

$$\frac{2\sqrt{6}}{2}\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

Annulla 2 u 2.

$$\sqrt{6}\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \sqrt{\frac{2}{5}} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{2}}{\sqrt{5}}.

$$\sqrt{6}\times \frac{\sqrt{2}}{\sqrt{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

Irrazzjonalizza d-denominatur tal-\frac{\sqrt{2}}{\sqrt{5}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{5}.

$$\sqrt{6}\times \frac{\sqrt{2}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}\left(-\frac{1}{8}\right)\sqrt{15}$$

Il-kwadrat ta' \sqrt{5} huwa 5.

$$\sqrt{6}\times \frac{\sqrt{2}\sqrt{5}}{5}\left(-\frac{1}{8}\right)\sqrt{15}$$

Biex timmultiplika \sqrt{2} u \sqrt{5}, immultiplika n-numri taħt l-għerq kwadrat.

$$\sqrt{6}\times \frac{\sqrt{10}}{5}\left(-\frac{1}{8}\right)\sqrt{15}$$

Esprimi \sqrt{6}\times \frac{\sqrt{10}}{5} bħala frazzjoni waħda.

$$\frac{\sqrt{6}\sqrt{10}}{5}\left(-\frac{1}{8}\right)\sqrt{15}$$

Immultiplika \frac{\sqrt{6}\sqrt{10}}{5} b'-\frac{1}{8} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

$$\frac{-\sqrt{6}\sqrt{10}}{5\times 8}\sqrt{15}$$

Esprimi \frac{-\sqrt{6}\sqrt{10}}{5\times 8}\sqrt{15} bħala frazzjoni waħda.

$$\frac{-\sqrt{6}\sqrt{10}\sqrt{15}}{5\times 8}$$

Biex timmultiplika \sqrt{6} u \sqrt{10}, immultiplika n-numri taħt l-għerq kwadrat.

$$\frac{-\sqrt{60}\sqrt{15}}{5\times 8}$$

Iffattura 60=15\times 4. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{15\times 4} bħala l-prodott tal-għeruq kwadrati \sqrt{15}\sqrt{4}.

$$\frac{-\sqrt{15}\sqrt{4}\sqrt{15}}{5\times 8}$$

Immultiplika \sqrt{15} u \sqrt{15} biex tikseb 15.

$$\frac{-15\sqrt{4}}{5\times 8}$$

Immultiplika 5 u 8 biex tikseb 40.

$$\frac{-15\sqrt{4}}{40}$$

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

$$\frac{-15\times 2}{40}$$

Immultiplika -15 u 2 biex tikseb -30.

$$\frac{-30}{40}$$

Naqqas il-frazzjoni \frac{-30}{40} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 10.

$$-\frac{3}{4}$$

Fattur

$$-\frac{3}{4} = -0.75$$