Issolvi 2/3sqrt{20}*(1/3sqrt{48})divsqrt{22/3}

$$\frac { 2 } { 3 } \sqrt { 20 } \times ( \frac { 1 } { 3 } \sqrt { 48 } ) \div \sqrt { 2 \frac { 2 } { 3 } }$$

Evalwa

$$\frac{4\sqrt{10}}{3}\approx 4.216370214$$

Passi tas-Soluzzjonijiet

Iffattura 20=2^{2}\times 5. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{2^{2}\times 5} bħala l-prodott tal-għeruq kwadrati \sqrt{2^{2}}\sqrt{5}. Ħu l-għerq kwadrat ta' 2^{2}.

$$\frac{\frac{2}{3}\times 2\sqrt{5}\times \frac{1}{3}\sqrt{48}}{\sqrt{\frac{2\times 3+2}{3}}}$$

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

$$\frac{\frac{2\times 2}{3}\sqrt{5}\times \frac{1}{3}\sqrt{48}}{\sqrt{\frac{2\times 3+2}{3}}}$$

Immultiplika 2 u 2 biex tikseb 4.

$$\frac{\frac{4}{3}\sqrt{5}\times \frac{1}{3}\sqrt{48}}{\sqrt{\frac{2\times 3+2}{3}}}$$

Immultiplika \frac{4}{3} b'\frac{1}{3} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

$$\frac{\frac{4\times 1}{3\times 3}\sqrt{5}\sqrt{48}}{\sqrt{\frac{2\times 3+2}{3}}}$$

Agħmel il-multiplikazzjonijiet fil-frazzjoni \frac{4\times 1}{3\times 3}.

$$\frac{\frac{4}{9}\sqrt{5}\sqrt{48}}{\sqrt{\frac{2\times 3+2}{3}}}$$

Iffattura 48=4^{2}\times 3. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{4^{2}\times 3} bħala l-prodott tal-għeruq kwadrati \sqrt{4^{2}}\sqrt{3}. Ħu l-għerq kwadrat ta' 4^{2}.

$$\frac{\frac{4}{9}\sqrt{5}\times 4\sqrt{3}}{\sqrt{\frac{2\times 3+2}{3}}}$$

Esprimi \frac{4}{9}\times 4 bħala frazzjoni waħda.

$$\frac{\frac{4\times 4}{9}\sqrt{5}\sqrt{3}}{\sqrt{\frac{2\times 3+2}{3}}}$$

Immultiplika 4 u 4 biex tikseb 16.

$$\frac{\frac{16}{9}\sqrt{5}\sqrt{3}}{\sqrt{\frac{2\times 3+2}{3}}}$$

Biex timmultiplika \sqrt{5} u \sqrt{3}, immultiplika n-numri taħt l-għerq kwadrat.

$$\frac{\frac{16}{9}\sqrt{15}}{\sqrt{\frac{2\times 3+2}{3}}}$$

Immultiplika 2 u 3 biex tikseb 6.

$$\frac{\frac{16}{9}\sqrt{15}}{\sqrt{\frac{6+2}{3}}}$$

Żid 6 u 2 biex tikseb 8.

$$\frac{\frac{16}{9}\sqrt{15}}{\sqrt{\frac{8}{3}}}$$

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

$$\frac{\frac{16}{9}\sqrt{15}}{\frac{\sqrt{8}}{\sqrt{3}}}$$

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}.

$$\frac{\frac{16}{9}\sqrt{15}}{\frac{2\sqrt{2}}{\sqrt{3}}}$$

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

$$\frac{\frac{16}{9}\sqrt{15}}{\frac{2\sqrt{2}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}}$$

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

$$\frac{\frac{16}{9}\sqrt{15}}{\frac{2\sqrt{2}\sqrt{3}}{3}}$$

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

$$\frac{\frac{16}{9}\sqrt{15}}{\frac{2\sqrt{6}}{3}}$$

Iddividi \frac{16}{9}\sqrt{15} b'\frac{2\sqrt{6}}{3} billi timmultiplika \frac{16}{9}\sqrt{15} bir-reċiproku ta' \frac{2\sqrt{6}}{3}.

$$\frac{\frac{16}{9}\sqrt{15}\times 3}{2\sqrt{6}}$$

Irrazzjonalizza d-denominatur tal-\frac{\frac{16}{9}\sqrt{15}\times 3}{2\sqrt{6}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{6}.

$$\frac{\frac{16}{9}\sqrt{15}\times 3\sqrt{6}}{2\left(\sqrt{6}\right)^{2}}$$

Il-kwadrat ta' \sqrt{6} huwa 6.

$$\frac{\frac{16}{9}\sqrt{15}\times 3\sqrt{6}}{2\times 6}$$

Esprimi \frac{16}{9}\times 3 bħala frazzjoni waħda.

$$\frac{\frac{16\times 3}{9}\sqrt{15}\sqrt{6}}{2\times 6}$$

Immultiplika 16 u 3 biex tikseb 48.

$$\frac{\frac{48}{9}\sqrt{15}\sqrt{6}}{2\times 6}$$

Naqqas il-frazzjoni \frac{48}{9} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 3.

$$\frac{\frac{16}{3}\sqrt{15}\sqrt{6}}{2\times 6}$$

Biex timmultiplika \sqrt{15} u \sqrt{6}, immultiplika n-numri taħt l-għerq kwadrat.

$$\frac{\frac{16}{3}\sqrt{90}}{2\times 6}$$

Immultiplika 2 u 6 biex tikseb 12.

$$\frac{\frac{16}{3}\sqrt{90}}{12}$$

Iffattura 90=3^{2}\times 10. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{3^{2}\times 10} bħala l-prodott tal-għeruq kwadrati \sqrt{3^{2}}\sqrt{10}. Ħu l-għerq kwadrat ta' 3^{2}.

$$\frac{\frac{16}{3}\times 3\sqrt{10}}{12}$$

Annulla 3 u 3.

$$\frac{16\sqrt{10}}{12}$$

Iddividi 16\sqrt{10} b'12 biex tikseb\frac{4}{3}\sqrt{10}.

$$\frac{4}{3}\sqrt{10}$$