Whakaoti i te frac{sqrt{2}}{frac{sqrt{5}}{3}}=x/sqrt{5/sqrt{6}}

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

Whakaoti mō x

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

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakawehe \sqrt{2} ki te \frac{\sqrt{5}}{3} mā te whakarea \sqrt{2} ki te tau huripoki o \frac{\sqrt{5}}{3}.

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

Whakangāwaritia te tauraro o \frac{\sqrt{2}\times 3}{\sqrt{5}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{5}.

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

Ko te pūrua o \sqrt{5} ko 5.

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

Hei whakarea \sqrt{2} me \sqrt{5}, whakareatia ngā tau i raro i te pūtake rua.

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

Whakawehe x ki te \frac{\sqrt{5}}{\sqrt{6}} mā te whakarea x ki te tau huripoki o \frac{\sqrt{5}}{\sqrt{6}}.

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

Whakangāwaritia te tauraro o \frac{x\sqrt{6}}{\sqrt{5}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{5}.

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

Ko te pūrua o \sqrt{5} ko 5.

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

Hei whakarea \sqrt{6} me \sqrt{5}, whakareatia ngā tau i raro i te pūtake rua.

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

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

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

Whakareatia ngā taha e rua o te whārite ki te 5.

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

He hanga arowhānui tō te whārite.

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

Whakawehea ngā taha e rua ki te \sqrt{30}.

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

Mā te whakawehe ki te \sqrt{30} ka wetekia te whakareanga ki te \sqrt{30}.

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

Whakawehe 3\sqrt{10} ki te \sqrt{30}.

$$x=\sqrt{3}$$