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

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

Evalwa

$$-3$$

Passi tas-Soluzzjonijiet

Immultiplika 2 u 3 biex tikseb 6.

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

Żid 6 u 2 biex tikseb 8.

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

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

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

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}.

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

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

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

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

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

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

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

Annulla 3 u 3.

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

Iddividi 2\sqrt{6} b'\frac{1}{2} billi timmultiplika 2\sqrt{6} bir-reċiproku ta' \frac{1}{2}.

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

Immultiplika 2 u 2 biex tikseb 4.

$$4\sqrt{6}\sqrt{\frac{2}{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

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

$$4\sqrt{6}\times \frac{\sqrt{2}}{\sqrt{5}}\left(-\frac{1}{8}\right)\sqrt{15}$$

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

$$4\sqrt{6}\times \frac{\sqrt{2}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}\left(-\frac{1}{8}\right)\sqrt{15}$$

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

$$4\sqrt{6}\times \frac{\sqrt{2}\sqrt{5}}{5}\left(-\frac{1}{8}\right)\sqrt{15}$$

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

$$4\sqrt{6}\times \frac{\sqrt{10}}{5}\left(-\frac{1}{8}\right)\sqrt{15}$$

Esprimi 4\left(-\frac{1}{8}\right) bħala frazzjoni waħda.

$$\frac{4\left(-1\right)}{8}\sqrt{6}\times \frac{\sqrt{10}}{5}\sqrt{15}$$

Immultiplika 4 u -1 biex tikseb -4.

$$\frac{-4}{8}\sqrt{6}\times \frac{\sqrt{10}}{5}\sqrt{15}$$

Naqqas il-frazzjoni \frac{-4}{8} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 4.

$$-\frac{1}{2}\sqrt{6}\times \frac{\sqrt{10}}{5}\sqrt{15}$$

Immultiplika -\frac{1}{2} b'\frac{\sqrt{10}}{5} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

$$\frac{-\sqrt{10}}{2\times 5}\sqrt{6}\sqrt{15}$$

Esprimi \frac{-\sqrt{10}}{2\times 5}\sqrt{15} bħala frazzjoni waħda.

$$\frac{-\sqrt{10}\sqrt{15}}{2\times 5}\sqrt{6}$$

Biex timmultiplika \sqrt{10} u \sqrt{15}, immultiplika n-numri taħt l-għerq kwadrat.

$$\frac{-\sqrt{150}}{2\times 5}\sqrt{6}$$

Immultiplika 2 u 5 biex tikseb 10.

$$\frac{-\sqrt{150}}{10}\sqrt{6}$$

Iffattura 150=5^{2}\times 6. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{5^{2}\times 6} bħala l-prodott tal-għeruq kwadrati \sqrt{5^{2}}\sqrt{6}. Ħu l-għerq kwadrat ta' 5^{2}.

$$\frac{-5\sqrt{6}}{10}\sqrt{6}$$

Iddividi -5\sqrt{6} b'10 biex tikseb-\frac{1}{2}\sqrt{6}.

$$-\frac{1}{2}\sqrt{6}\sqrt{6}$$

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

$$-\frac{1}{2}\times 6$$

Esprimi -\frac{1}{2}\times 6 bħala frazzjoni waħda.

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

Iddividi -6 b'2 biex tikseb-3.

$$-3$$

Fattur

$$-3$$