Issolvi 2sqrt{3}divsqrt{7/3}*sqrt{7/5}

$$2 \sqrt{ 3 } \div \sqrt{ \frac{ 7 }{ 3 } } \times \sqrt{ \frac{ 7 }{ 5 } }$$

Evalwa

$$\frac{6\sqrt{5}}{5}\approx 2.683281573$$

Passi tas-Soluzzjonijiet

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \sqrt{\frac{7}{3}} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{7}}{\sqrt{3}}.

$$\frac{2\sqrt{3}}{\frac{\sqrt{7}}{\sqrt{3}}}\sqrt{\frac{7}{5}}$$

Irrazzjonalizza d-denominatur tal-\frac{\sqrt{7}}{\sqrt{3}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{3}.

$$\frac{2\sqrt{3}}{\frac{\sqrt{7}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}}\sqrt{\frac{7}{5}}$$

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

$$\frac{2\sqrt{3}}{\frac{\sqrt{7}\sqrt{3}}{3}}\sqrt{\frac{7}{5}}$$

Biex timmultiplika \sqrt{7} u \sqrt{3}, immultiplika n-numri taħt l-għerq kwadrat.

$$\frac{2\sqrt{3}}{\frac{\sqrt{21}}{3}}\sqrt{\frac{7}{5}}$$

Iddividi 2\sqrt{3} b'\frac{\sqrt{21}}{3} billi timmultiplika 2\sqrt{3} bir-reċiproku ta' \frac{\sqrt{21}}{3}.

$$\frac{2\sqrt{3}\times 3}{\sqrt{21}}\sqrt{\frac{7}{5}}$$

Irrazzjonalizza d-denominatur tal-\frac{2\sqrt{3}\times 3}{\sqrt{21}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{21}.

$$\frac{2\sqrt{3}\times 3\sqrt{21}}{\left(\sqrt{21}\right)^{2}}\sqrt{\frac{7}{5}}$$

Il-kwadrat ta' \sqrt{21} huwa 21.

$$\frac{2\sqrt{3}\times 3\sqrt{21}}{21}\sqrt{\frac{7}{5}}$$

Immultiplika 2 u 3 biex tikseb 6.

$$\frac{6\sqrt{3}\sqrt{21}}{21}\sqrt{\frac{7}{5}}$$

Iffattura 21=3\times 7. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{3\times 7} bħala l-prodott tal-għeruq kwadrati \sqrt{3}\sqrt{7}.

$$\frac{6\sqrt{3}\sqrt{3}\sqrt{7}}{21}\sqrt{\frac{7}{5}}$$

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

$$\frac{6\times 3\sqrt{7}}{21}\sqrt{\frac{7}{5}}$$

Immultiplika 6 u 3 biex tikseb 18.

$$\frac{18\sqrt{7}}{21}\sqrt{\frac{7}{5}}$$

Iddividi 18\sqrt{7} b'21 biex tikseb\frac{6}{7}\sqrt{7}.

$$\frac{6}{7}\sqrt{7}\sqrt{\frac{7}{5}}$$

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \sqrt{\frac{7}{5}} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{7}}{\sqrt{5}}.

$$\frac{6}{7}\sqrt{7}\times \frac{\sqrt{7}}{\sqrt{5}}$$

Irrazzjonalizza d-denominatur tal-\frac{\sqrt{7}}{\sqrt{5}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{5}.

$$\frac{6}{7}\sqrt{7}\times \frac{\sqrt{7}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

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

$$\frac{6}{7}\sqrt{7}\times \frac{\sqrt{7}\sqrt{5}}{5}$$

Biex timmultiplika \sqrt{7} u \sqrt{5}, immultiplika n-numri taħt l-għerq kwadrat.

$$\frac{6}{7}\sqrt{7}\times \frac{\sqrt{35}}{5}$$

Immultiplika \frac{6}{7} b'\frac{\sqrt{35}}{5} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

$$\frac{6\sqrt{35}}{7\times 5}\sqrt{7}$$

Immultiplika 7 u 5 biex tikseb 35.

$$\frac{6\sqrt{35}}{35}\sqrt{7}$$

Esprimi \frac{6\sqrt{35}}{35}\sqrt{7} bħala frazzjoni waħda.

$$\frac{6\sqrt{35}\sqrt{7}}{35}$$

Iffattura 35=7\times 5. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{7\times 5} bħala l-prodott tal-għeruq kwadrati \sqrt{7}\sqrt{5}.

$$\frac{6\sqrt{7}\sqrt{5}\sqrt{7}}{35}$$

Immultiplika \sqrt{7} u \sqrt{7} biex tikseb 7.

$$\frac{6\times 7\sqrt{5}}{35}$$

Immultiplika 6 u 7 biex tikseb 42.

$$\frac{42\sqrt{5}}{35}$$

Iddividi 42\sqrt{5} b'35 biex tikseb\frac{6}{5}\sqrt{5}.

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