Issolvi sqrt{6.67*10^-11*1.99*10^30/4.59*10^10}

$$\sqrt { \frac { 6.67 \times 10 ^ { - 11 } \times 1.99 \times 10 ^ { 30 } } { 4.59 \times 10 ^ { 10 } } }$$

Evalwa

$$\frac{1000\sqrt{67693830}}{153}\approx 53775.333493849$$

Passi tas-Soluzzjonijiet

Biex timmultiplika l-qawwa tal-istess bażi, żid l-esponenti tagħhom. Żid -11 u 30 biex tikseb 19.

$$\sqrt{\frac{6.67\times 10^{19}\times 1.99}{4.59\times 10^{10}}}$$

Annulla 10^{10} fin-numeratur u d-denominatur.

$$\sqrt{\frac{1.99\times 6.67\times 10^{9}}{4.59}}$$

Immultiplika 1.99 u 6.67 biex tikseb 13.2733.

$$\sqrt{\frac{13.2733\times 10^{9}}{4.59}}$$

Ikkalkula 10 bil-power ta' 9 u tikseb 1000000000.

$$\sqrt{\frac{13.2733\times 1000000000}{4.59}}$$

Immultiplika 13.2733 u 1000000000 biex tikseb 13273300000.

$$\sqrt{\frac{13273300000}{4.59}}$$

Espandi \frac{13273300000}{4.59} billi timmultiplika kemm in-numeratur kif ukoll id-denominatur b'100.

$$\sqrt{\frac{1327330000000}{459}}$$

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \sqrt{\frac{1327330000000}{459}} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{1327330000000}}{\sqrt{459}}.

$$\frac{\sqrt{1327330000000}}{\sqrt{459}}$$

Iffattura 1327330000000=1000^{2}\times 1327330. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{1000^{2}\times 1327330} bħala l-prodott tal-għeruq kwadrati \sqrt{1000^{2}}\sqrt{1327330}. Ħu l-għerq kwadrat ta' 1000^{2}.

$$\frac{1000\sqrt{1327330}}{\sqrt{459}}$$

Iffattura 459=3^{2}\times 51. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{3^{2}\times 51} bħala l-prodott tal-għeruq kwadrati \sqrt{3^{2}}\sqrt{51}. Ħu l-għerq kwadrat ta' 3^{2}.

$$\frac{1000\sqrt{1327330}}{3\sqrt{51}}$$

Irrazzjonalizza d-denominatur tal-\frac{1000\sqrt{1327330}}{3\sqrt{51}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{51}.

$$\frac{1000\sqrt{1327330}\sqrt{51}}{3\left(\sqrt{51}\right)^{2}}$$

Il-kwadrat ta' \sqrt{51} huwa 51.

$$\frac{1000\sqrt{1327330}\sqrt{51}}{3\times 51}$$

Biex timmultiplika \sqrt{1327330} u \sqrt{51}, immultiplika n-numri taħt l-għerq kwadrat.

$$\frac{1000\sqrt{67693830}}{3\times 51}$$

Immultiplika 3 u 51 biex tikseb 153.

$$\frac{1000\sqrt{67693830}}{153}$$