Issolvi sqrt{1frac{2/3}}{sqrt{5/6}}

$$\frac{ \sqrt{ 1 \frac{ 2 }{ 3 } } }{ \sqrt{ \frac{ 5 }{ 6 } } }$$

Evalwa

$$\sqrt{2}\approx 1.414213562$$

Passi tas-Soluzzjonijiet

Immultiplika 1 u 3 biex tikseb 3.

$$\frac{\sqrt{\frac{3+2}{3}}}{\sqrt{\frac{5}{6}}}$$

Żid 3 u 2 biex tikseb 5.

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

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

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

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

$$\frac{\frac{\sqrt{5}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}}{\sqrt{\frac{5}{6}}}$$

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

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

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

$$\frac{\frac{\sqrt{15}}{3}}{\sqrt{\frac{5}{6}}}$$

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \sqrt{\frac{5}{6}} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{5}}{\sqrt{6}}.

$$\frac{\frac{\sqrt{15}}{3}}{\frac{\sqrt{5}}{\sqrt{6}}}$$

Irrazzjonalizza d-denominatur tal-\frac{\sqrt{5}}{\sqrt{6}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{6}.

$$\frac{\frac{\sqrt{15}}{3}}{\frac{\sqrt{5}\sqrt{6}}{\left(\sqrt{6}\right)^{2}}}$$

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

$$\frac{\frac{\sqrt{15}}{3}}{\frac{\sqrt{5}\sqrt{6}}{6}}$$

Biex timmultiplika \sqrt{5} u \sqrt{6}, immultiplika n-numri taħt l-għerq kwadrat.

$$\frac{\frac{\sqrt{15}}{3}}{\frac{\sqrt{30}}{6}}$$

Iddividi \frac{\sqrt{15}}{3} b'\frac{\sqrt{30}}{6} billi timmultiplika \frac{\sqrt{15}}{3} bir-reċiproku ta' \frac{\sqrt{30}}{6}.

$$\frac{\sqrt{15}\times 6}{3\sqrt{30}}$$

Annulla 3 fin-numeratur u d-denominatur.

$$\frac{2\sqrt{15}}{\sqrt{30}}$$

Irrazzjonalizza d-denominatur tal-\frac{2\sqrt{15}}{\sqrt{30}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{30}.

$$\frac{2\sqrt{15}\sqrt{30}}{\left(\sqrt{30}\right)^{2}}$$

Il-kwadrat ta' \sqrt{30} huwa 30.

$$\frac{2\sqrt{15}\sqrt{30}}{30}$$

Iffattura 30=15\times 2. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{15\times 2} bħala l-prodott tal-għeruq kwadrati \sqrt{15}\sqrt{2}.

$$\frac{2\sqrt{15}\sqrt{15}\sqrt{2}}{30}$$

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

$$\frac{2\times 15\sqrt{2}}{30}$$

Immultiplika 2 u 15 biex tikseb 30.

$$\frac{30\sqrt{2}}{30}$$

Annulla 30 u 30.

$$\sqrt{2}$$