Issolvi frac{sqrt{2}}{sqrt{5}}*frac{(sqrt{5})^2}{sqrt{3}}

$$\frac { \sqrt { 2 } } { \sqrt { 5 } } \times \frac { ( \sqrt { 5 } ) ^ { 2 } } { \sqrt { 3 } }$$

Evalwa

$$\frac{\sqrt{30}}{3}\approx 1.825741858$$

Passi tas-Soluzzjonijiet

Irrazzjonalizza d-denominatur tal-\frac{\sqrt{2}}{\sqrt{5}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{5}.

$$\frac{\sqrt{2}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}\times \frac{\left(\sqrt{5}\right)^{2}}{\sqrt{3}}$$

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

$$\frac{\sqrt{2}\sqrt{5}}{5}\times \frac{\left(\sqrt{5}\right)^{2}}{\sqrt{3}}$$

Biex timmultiplika \sqrt{2} u \sqrt{5}, immultiplika n-numri taħt l-għerq kwadrat.

$$\frac{\sqrt{10}}{5}\times \frac{\left(\sqrt{5}\right)^{2}}{\sqrt{3}}$$

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

$$\frac{\sqrt{10}}{5}\times \frac{5}{\sqrt{3}}$$

Irrazzjonalizza d-denominatur tal-\frac{5}{\sqrt{3}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{3}.

$$\frac{\sqrt{10}}{5}\times \frac{5\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

Il-kwadrat ta' \sqrt{3} huwa 3.

$$\frac{\sqrt{10}}{5}\times \frac{5\sqrt{3}}{3}$$

Immultiplika \frac{\sqrt{10}}{5} b'\frac{5\sqrt{3}}{3} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

$$\frac{\sqrt{10}\times 5\sqrt{3}}{5\times 3}$$

Annulla 5 fin-numeratur u d-denominatur.

$$\frac{\sqrt{3}\sqrt{10}}{3}$$

Biex timmultiplika \sqrt{3} u \sqrt{10}, immultiplika n-numri taħt l-għerq kwadrat.

$$\frac{\sqrt{30}}{3}$$