Issolvi sqrt{832*468/21*1001}

$$\sqrt { \frac { 832 \times 468 } { 21 \times 1001 } }$$

Evalwa

$$\frac{16\sqrt{429}}{77}\approx 4.303857699$$

Passi tas-Soluzzjonijiet

Annulla 3\times 13 fin-numeratur u d-denominatur.

$$\sqrt{\frac{64\times 156}{7\times 77}}$$

Immultiplika 64 u 156 biex tikseb 9984.

$$\sqrt{\frac{9984}{7\times 77}}$$

Immultiplika 7 u 77 biex tikseb 539.

$$\sqrt{\frac{9984}{539}}$$

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \sqrt{\frac{9984}{539}} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{9984}}{\sqrt{539}}.

$$\frac{\sqrt{9984}}{\sqrt{539}}$$

Iffattura 9984=16^{2}\times 39. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{16^{2}\times 39} bħala l-prodott tal-għeruq kwadrati \sqrt{16^{2}}\sqrt{39}. Ħu l-għerq kwadrat ta' 16^{2}.

$$\frac{16\sqrt{39}}{\sqrt{539}}$$

Iffattura 539=7^{2}\times 11. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{7^{2}\times 11} bħala l-prodott tal-għeruq kwadrati \sqrt{7^{2}}\sqrt{11}. Ħu l-għerq kwadrat ta' 7^{2}.

$$\frac{16\sqrt{39}}{7\sqrt{11}}$$

Irrazzjonalizza d-denominatur tal-\frac{16\sqrt{39}}{7\sqrt{11}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{11}.

$$\frac{16\sqrt{39}\sqrt{11}}{7\left(\sqrt{11}\right)^{2}}$$

Il-kwadrat ta' \sqrt{11} huwa 11.

$$\frac{16\sqrt{39}\sqrt{11}}{7\times 11}$$

Biex timmultiplika \sqrt{39} u \sqrt{11}, immultiplika n-numri taħt l-għerq kwadrat.

$$\frac{16\sqrt{429}}{7\times 11}$$

Immultiplika 7 u 11 biex tikseb 77.

$$\frac{16\sqrt{429}}{77}$$