Issolvi sqrt{6.67*10^-115.98*10^24/900+6378}

$$\sqrt{ \frac{ 6.67 \times { 10 }^{ -11 } 5.98 \times { 10 }^{ 24 } }{ 900+6378 } }$$

Evalwa

$$\frac{230000\sqrt{13719030}}{3639}\approx 234103.271767306$$

Passi tas-Soluzzjonijiet

Biex timmultiplika l-qawwa tal-istess bażi, żid l-esponenti tagħhom. Żid -11 u 24 biex tikseb 13.

$$\sqrt{\frac{6.67\times 10^{13}\times 5.98}{900+6378}}$$

Ikkalkula 10 bil-power ta' 13 u tikseb 10000000000000.

$$\sqrt{\frac{6.67\times 10000000000000\times 5.98}{900+6378}}$$

Immultiplika 6.67 u 10000000000000 biex tikseb 66700000000000.

$$\sqrt{\frac{66700000000000\times 5.98}{900+6378}}$$

Immultiplika 66700000000000 u 5.98 biex tikseb 398866000000000.

$$\sqrt{\frac{398866000000000}{900+6378}}$$

Żid 900 u 6378 biex tikseb 7278.

$$\sqrt{\frac{398866000000000}{7278}}$$

Naqqas il-frazzjoni \frac{398866000000000}{7278} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 2.

$$\sqrt{\frac{199433000000000}{3639}}$$

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \sqrt{\frac{199433000000000}{3639}} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{199433000000000}}{\sqrt{3639}}.

$$\frac{\sqrt{199433000000000}}{\sqrt{3639}}$$

Iffattura 199433000000000=230000^{2}\times 3770. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{230000^{2}\times 3770} bħala l-prodott tal-għeruq kwadrati \sqrt{230000^{2}}\sqrt{3770}. Ħu l-għerq kwadrat ta' 230000^{2}.

$$\frac{230000\sqrt{3770}}{\sqrt{3639}}$$

Irrazzjonalizza d-denominatur tal-\frac{230000\sqrt{3770}}{\sqrt{3639}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{3639}.

$$\frac{230000\sqrt{3770}\sqrt{3639}}{\left(\sqrt{3639}\right)^{2}}$$

Il-kwadrat ta' \sqrt{3639} huwa 3639.

$$\frac{230000\sqrt{3770}\sqrt{3639}}{3639}$$

Biex timmultiplika \sqrt{3770} u \sqrt{3639}, immultiplika n-numri taħt l-għerq kwadrat.

$$\frac{230000\sqrt{13719030}}{3639}$$