Issolvi frac{sqrt{2}}{frac{sqrt{5}}{3}}=x/sqrt{5/sqrt{6}}

$$\frac { \sqrt { 2 } } { \frac { \sqrt { 5 } } { 3 } } = \frac { x } { \frac { \sqrt { 5 } } { \sqrt { 6 } } }$$

Solvi għal x

$$x=\sqrt{3}\approx 1.732050808$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Iddividi \sqrt{2} b'\frac{\sqrt{5}}{3} billi timmultiplika \sqrt{2} bir-reċiproku ta' \frac{\sqrt{5}}{3}.

$$\frac{\sqrt{2}\times 3}{\sqrt{5}}=\frac{x}{\frac{\sqrt{5}}{\sqrt{6}}}$$

Irrazzjonalizza d-denominatur tal-\frac{\sqrt{2}\times 3}{\sqrt{5}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{5}.

$$\frac{\sqrt{2}\times 3\sqrt{5}}{\left(\sqrt{5}\right)^{2}}=\frac{x}{\frac{\sqrt{5}}{\sqrt{6}}}$$

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

$$\frac{\sqrt{2}\times 3\sqrt{5}}{5}=\frac{x}{\frac{\sqrt{5}}{\sqrt{6}}}$$

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

$$\frac{\sqrt{10}\times 3}{5}=\frac{x}{\frac{\sqrt{5}}{\sqrt{6}}}$$

Iddividi x b'\frac{\sqrt{5}}{\sqrt{6}} billi timmultiplika x bir-reċiproku ta' \frac{\sqrt{5}}{\sqrt{6}}.

$$\frac{\sqrt{10}\times 3}{5}=\frac{x\sqrt{6}}{\sqrt{5}}$$

Irrazzjonalizza d-denominatur tal-\frac{x\sqrt{6}}{\sqrt{5}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{5}.

$$\frac{\sqrt{10}\times 3}{5}=\frac{x\sqrt{6}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

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

$$\frac{\sqrt{10}\times 3}{5}=\frac{x\sqrt{6}\sqrt{5}}{5}$$

Biex timmultiplika \sqrt{6} u \sqrt{5}, immultiplika n-numri taħt l-għerq kwadrat.

$$\frac{\sqrt{10}\times 3}{5}=\frac{x\sqrt{30}}{5}$$

Ibdel in-naħat sabiex it-termini varjabbli kollha jkunu fuq in-naħa tax-xellug.

$$\frac{x\sqrt{30}}{5}=\frac{\sqrt{10}\times 3}{5}$$

Immultiplika ż-żewġ naħat tal-ekwazzjoni b'5.

$$x\sqrt{30}=\sqrt{10}\times 3$$

L-ekwazzjoni hija f'forma standard.

$$\sqrt{30}x=3\sqrt{10}$$

Iddividi ż-żewġ naħat b'\sqrt{30}.

$$\frac{\sqrt{30}x}{\sqrt{30}}=\frac{3\sqrt{10}}{\sqrt{30}}$$

Meta tiddividi b'\sqrt{30} titneħħa l-multiplikazzjoni b'\sqrt{30}.

$$x=\frac{3\sqrt{10}}{\sqrt{30}}$$

Iddividi 3\sqrt{10} b'\sqrt{30}.

$$x=\sqrt{3}$$