Issolvi 2/sqrt{5}frac{1sqrt{3}}{2}-1/sqrt{5}1/2

$$\frac{ 2 }{ \sqrt{ 5 } } \frac{ 1 \sqrt{ 3 } }{ 2 } - \frac{ 1 }{ \sqrt{ 5 } } \frac{ 1 }{ 2 }$$

Evalwa

$$\frac{\sqrt{15}}{5}-\frac{\sqrt{5}}{10}\approx 0.550989871$$

Passi Qosra tas-Soluzzjonijiet

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

$$\frac{2\sqrt{5}}{\left(\sqrt{5}\right)^{2}}\times \frac{1\sqrt{3}}{2}-\frac{1}{\sqrt{5}}\times \frac{1}{2}$$

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

$$\frac{2\sqrt{5}}{5}\times \frac{1\sqrt{3}}{2}-\frac{1}{\sqrt{5}}\times \frac{1}{2}$$

Immultiplika \frac{2\sqrt{5}}{5} b'\frac{1\sqrt{3}}{2} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

$$\frac{2\sqrt{5}\times 1\sqrt{3}}{5\times 2}-\frac{1}{\sqrt{5}}\times \frac{1}{2}$$

Annulla 2 fin-numeratur u d-denominatur.

$$\frac{\sqrt{3}\sqrt{5}}{5}-\frac{1}{\sqrt{5}}\times \frac{1}{2}$$

Irrazzjonalizza d-denominatur tal-\frac{1}{\sqrt{5}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{5}.

$$\frac{\sqrt{3}\sqrt{5}}{5}-\frac{\sqrt{5}}{\left(\sqrt{5}\right)^{2}}\times \frac{1}{2}$$

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

$$\frac{\sqrt{3}\sqrt{5}}{5}-\frac{\sqrt{5}}{5}\times \frac{1}{2}$$

Immultiplika \frac{\sqrt{5}}{5} b'\frac{1}{2} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

$$\frac{\sqrt{3}\sqrt{5}}{5}-\frac{\sqrt{5}}{5\times 2}$$

Immultiplika 5 u 2 biex tikseb 10.

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

Biex iżżid jew tnaqqas l-espressjonijiet, espandihom biex id-denominaturi tagħhom ikunu l-istess. L-inqas multiplu komuni ta' 5 u 10 huwa 10. Immultiplika \frac{\sqrt{3}\sqrt{5}}{5} b'\frac{2}{2}.

$$\frac{2\sqrt{3}\sqrt{5}}{10}-\frac{\sqrt{5}}{10}$$

Billi \frac{2\sqrt{3}\sqrt{5}}{10} u \frac{\sqrt{5}}{10} għandhom l-istess denominatur, naqqashom billi tnaqqas in-numeraturi tagħhom.

$$\frac{2\sqrt{3}\sqrt{5}-\sqrt{5}}{10}$$

Agħmel il-multiplikazzjonijiet fi 2\sqrt{3}\sqrt{5}-\sqrt{5}.

$$\frac{2\sqrt{15}-\sqrt{5}}{10}$$

Fattur

$$\frac{\sqrt{5} {(2 \sqrt{3} - 1)}}{10} = 0.5509898714915045$$