Issolvi frac{sqrt{56^2-46^2}}{0,25*sqrt{10}}

$$\frac { \sqrt { 56 ^ { 2 } - 46 ^ { 2 } } } { 0,25 \cdot \sqrt { 10 } }$$

Evalwa

$$4\sqrt{102}\approx 40.398019753$$

Passi tas-Soluzzjonijiet

Ikkalkula 56 bil-power ta' 2 u tikseb 3136.

$$\frac{\sqrt{3136-46^{2}}}{0.25\sqrt{10}}$$

Ikkalkula 46 bil-power ta' 2 u tikseb 2116.

$$\frac{\sqrt{3136-2116}}{0.25\sqrt{10}}$$

Naqqas 2116 minn 3136 biex tikseb 1020.

$$\frac{\sqrt{1020}}{0.25\sqrt{10}}$$

Iffattura 1020=2^{2}\times 255. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{2^{2}\times 255} bħala l-prodott tal-għeruq kwadrati \sqrt{2^{2}}\sqrt{255}. Ħu l-għerq kwadrat ta' 2^{2}.

$$\frac{2\sqrt{255}}{0.25\sqrt{10}}$$

Irrazzjonalizza d-denominatur tal-\frac{2\sqrt{255}}{0.25\sqrt{10}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{10}.

$$\frac{2\sqrt{255}\sqrt{10}}{0.25\left(\sqrt{10}\right)^{2}}$$

Il-kwadrat ta' \sqrt{10} huwa 10.

$$\frac{2\sqrt{255}\sqrt{10}}{0.25\times 10}$$

Biex timmultiplika \sqrt{255} u \sqrt{10}, immultiplika n-numri taħt l-għerq kwadrat.

$$\frac{2\sqrt{2550}}{0.25\times 10}$$

Immultiplika 0.25 u 10 biex tikseb 2.5.

$$\frac{2\sqrt{2550}}{2.5}$$

Iffattura 2550=5^{2}\times 102. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{5^{2}\times 102} bħala l-prodott tal-għeruq kwadrati \sqrt{5^{2}}\sqrt{102}. Ħu l-għerq kwadrat ta' 5^{2}.

$$\frac{2\times 5\sqrt{102}}{2.5}$$

Immultiplika 2 u 5 biex tikseb 10.

$$\frac{10\sqrt{102}}{2.5}$$

Iddividi 10\sqrt{102} b'2.5 biex tikseb4\sqrt{102}.

$$4\sqrt{102}$$