Issolvi frac{2*sqrt{343}+sqrt{125}}{sqrt{5}}

$$\frac { 2 \cdot \sqrt { 343 } + \sqrt { 125 } } { \sqrt { 5 } }$$

Evalwa

$$\frac{14\sqrt{35}}{5}+5\approx 21.565023393$$

Passi tas-Soluzzjonijiet

Iffattura 343=7^{2}\times 7. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{7^{2}\times 7} bħala l-prodott tal-għeruq kwadrati \sqrt{7^{2}}\sqrt{7}. Ħu l-għerq kwadrat ta' 7^{2}.

$$\frac{2\times 7\sqrt{7}+\sqrt{125}}{\sqrt{5}}$$

Immultiplika 2 u 7 biex tikseb 14.

$$\frac{14\sqrt{7}+\sqrt{125}}{\sqrt{5}}$$

Iffattura 125=5^{2}\times 5. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{5^{2}\times 5} bħala l-prodott tal-għeruq kwadrati \sqrt{5^{2}}\sqrt{5}. Ħu l-għerq kwadrat ta' 5^{2}.

$$\frac{14\sqrt{7}+5\sqrt{5}}{\sqrt{5}}$$

Irrazzjonalizza d-denominatur tal-\frac{14\sqrt{7}+5\sqrt{5}}{\sqrt{5}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{5}.

$$\frac{\left(14\sqrt{7}+5\sqrt{5}\right)\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

Il-kwadrat ta' \sqrt{5} huwa 5.

$$\frac{\left(14\sqrt{7}+5\sqrt{5}\right)\sqrt{5}}{5}$$

Uża l-propjetà distributtiva biex timmultiplika 14\sqrt{7}+5\sqrt{5} b'\sqrt{5}.

$$\frac{14\sqrt{7}\sqrt{5}+5\left(\sqrt{5}\right)^{2}}{5}$$

Biex timmultiplika \sqrt{7} u \sqrt{5}, immultiplika n-numri taħt l-għerq kwadrat.

$$\frac{14\sqrt{35}+5\left(\sqrt{5}\right)^{2}}{5}$$

Il-kwadrat ta' \sqrt{5} huwa 5.

$$\frac{14\sqrt{35}+5\times 5}{5}$$

Immultiplika 5 u 5 biex tikseb 25.

$$\frac{14\sqrt{35}+25}{5}$$