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

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

Evalwa

$$1$$

Passi tas-Soluzzjonijiet

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \sqrt{\frac{5}{3}} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{5}}{\sqrt{3}}.

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

Irrazzjonalizza d-denominatur tal-\frac{\sqrt{5}}{\sqrt{3}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{3}.

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

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

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

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

$$\frac{\frac{\sqrt{15}}{3}}{\sqrt{\frac{7}{3}}}\sqrt{\frac{7}{5}}$$

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

$$\frac{\frac{\sqrt{15}}{3}}{\frac{\sqrt{7}}{\sqrt{3}}}\sqrt{\frac{7}{5}}$$

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

$$\frac{\frac{\sqrt{15}}{3}}{\frac{\sqrt{7}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}}\sqrt{\frac{7}{5}}$$

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

$$\frac{\frac{\sqrt{15}}{3}}{\frac{\sqrt{7}\sqrt{3}}{3}}\sqrt{\frac{7}{5}}$$

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

$$\frac{\frac{\sqrt{15}}{3}}{\frac{\sqrt{21}}{3}}\sqrt{\frac{7}{5}}$$

Iddividi \frac{\sqrt{15}}{3} b'\frac{\sqrt{21}}{3} billi timmultiplika \frac{\sqrt{15}}{3} bir-reċiproku ta' \frac{\sqrt{21}}{3}.

$$\frac{\sqrt{15}\times 3}{3\sqrt{21}}\sqrt{\frac{7}{5}}$$

Annulla 3 fin-numeratur u d-denominatur.

$$\frac{\sqrt{15}}{\sqrt{21}}\sqrt{\frac{7}{5}}$$

Irrazzjonalizza d-denominatur tal-\frac{\sqrt{15}}{\sqrt{21}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{21}.

$$\frac{\sqrt{15}\sqrt{21}}{\left(\sqrt{21}\right)^{2}}\sqrt{\frac{7}{5}}$$

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

$$\frac{\sqrt{15}\sqrt{21}}{21}\sqrt{\frac{7}{5}}$$

Biex timmultiplika \sqrt{15} u \sqrt{21}, immultiplika n-numri taħt l-għerq kwadrat.

$$\frac{\sqrt{315}}{21}\sqrt{\frac{7}{5}}$$

Iffattura 315=3^{2}\times 35. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{3^{2}\times 35} bħala l-prodott tal-għeruq kwadrati \sqrt{3^{2}}\sqrt{35}. Ħu l-għerq kwadrat ta' 3^{2}.

$$\frac{3\sqrt{35}}{21}\sqrt{\frac{7}{5}}$$

Iddividi 3\sqrt{35} b'21 biex tikseb\frac{1}{7}\sqrt{35}.

$$\frac{1}{7}\sqrt{35}\sqrt{\frac{7}{5}}$$

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

$$\frac{1}{7}\sqrt{35}\times \frac{\sqrt{7}}{\sqrt{5}}$$

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

$$\frac{1}{7}\sqrt{35}\times \frac{\sqrt{7}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

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

$$\frac{1}{7}\sqrt{35}\times \frac{\sqrt{7}\sqrt{5}}{5}$$

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

$$\frac{1}{7}\sqrt{35}\times \frac{\sqrt{35}}{5}$$

Immultiplika \frac{1}{7} b'\frac{\sqrt{35}}{5} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

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

Immultiplika 7 u 5 biex tikseb 35.

$$\frac{\sqrt{35}}{35}\sqrt{35}$$

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

$$\frac{\sqrt{35}\sqrt{35}}{35}$$

Immultiplika \sqrt{35} u \sqrt{35} biex tikseb 35.

$$\frac{35}{35}$$

Iddividi 35 b'35 biex tikseb1.

$$1$$

Fattur

$$1$$