Datrys 3sqrt{22/3}div1/2sqrt{2/5}-1/8sqrt{15}

$$3 \sqrt{ 2 \frac{ 2 }{ 3 } } \div \frac{ 1 }{ 2 } \sqrt{ \frac{ 2 }{ 5 } } - \frac{ 1 }{ 8 } \sqrt{ 15 }$$

Enrhifo

$$\frac{59\sqrt{15}}{40}\approx 5.712650436$$

Camau Ateb

Lluosi 2 a 3 i gael 6.

$$\frac{3\sqrt{\frac{6+2}{3}}}{\frac{1}{2}}\sqrt{\frac{2}{5}}-\frac{1}{8}\sqrt{15}$$

Adio 6 a 2 i gael 8.

$$\frac{3\sqrt{\frac{8}{3}}}{\frac{1}{2}}\sqrt{\frac{2}{5}}-\frac{1}{8}\sqrt{15}$$

Ailysgrifennu ail isradd y rhaniad \sqrt{\frac{8}{3}} fel rhaniad ail israddau \frac{\sqrt{8}}{\sqrt{3}}.

$$\frac{3\times \frac{\sqrt{8}}{\sqrt{3}}}{\frac{1}{2}}\sqrt{\frac{2}{5}}-\frac{1}{8}\sqrt{15}$$

Ffactora 8=2^{2}\times 2. Ailysgrifennu ail isradd y lluoswm \sqrt{2^{2}\times 2} fel lluoswm ail israddau \sqrt{2^{2}}\sqrt{2}. Cymryd isradd 2^{2}.

$$\frac{3\times \frac{2\sqrt{2}}{\sqrt{3}}}{\frac{1}{2}}\sqrt{\frac{2}{5}}-\frac{1}{8}\sqrt{15}$$

Mae'n rhesymoli enwadur \frac{2\sqrt{2}}{\sqrt{3}} drwy luosi'r rhifiadur a'r enwadur â \sqrt{3}.

$$\frac{3\times \frac{2\sqrt{2}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}}{\frac{1}{2}}\sqrt{\frac{2}{5}}-\frac{1}{8}\sqrt{15}$$

Sgwâr \sqrt{3} yw 3.

$$\frac{3\times \frac{2\sqrt{2}\sqrt{3}}{3}}{\frac{1}{2}}\sqrt{\frac{2}{5}}-\frac{1}{8}\sqrt{15}$$

I luosi \sqrt{2} a \sqrt{3}, dylid lluosi'r rhifau dan yr ail isradd.

$$\frac{3\times \frac{2\sqrt{6}}{3}}{\frac{1}{2}}\sqrt{\frac{2}{5}}-\frac{1}{8}\sqrt{15}$$

Canslo 3 a 3.

$$\frac{2\sqrt{6}}{\frac{1}{2}}\sqrt{\frac{2}{5}}-\frac{1}{8}\sqrt{15}$$

Rhannwch 2\sqrt{6} â \frac{1}{2} drwy luosi 2\sqrt{6} â chilydd \frac{1}{2}.

$$2\sqrt{6}\times 2\sqrt{\frac{2}{5}}-\frac{1}{8}\sqrt{15}$$

Lluosi 2 a 2 i gael 4.

$$4\sqrt{6}\sqrt{\frac{2}{5}}-\frac{1}{8}\sqrt{15}$$

Ailysgrifennu ail isradd y rhaniad \sqrt{\frac{2}{5}} fel rhaniad ail israddau \frac{\sqrt{2}}{\sqrt{5}}.

$$4\sqrt{6}\times \frac{\sqrt{2}}{\sqrt{5}}-\frac{1}{8}\sqrt{15}$$

Mae'n rhesymoli enwadur \frac{\sqrt{2}}{\sqrt{5}} drwy luosi'r rhifiadur a'r enwadur â \sqrt{5}.

$$4\sqrt{6}\times \frac{\sqrt{2}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}-\frac{1}{8}\sqrt{15}$$

Sgwâr \sqrt{5} yw 5.

$$4\sqrt{6}\times \frac{\sqrt{2}\sqrt{5}}{5}-\frac{1}{8}\sqrt{15}$$

I luosi \sqrt{2} a \sqrt{5}, dylid lluosi'r rhifau dan yr ail isradd.

$$4\sqrt{6}\times \frac{\sqrt{10}}{5}-\frac{1}{8}\sqrt{15}$$

Mynegwch 4\times \frac{\sqrt{10}}{5} fel ffracsiwn unigol.

$$\frac{4\sqrt{10}}{5}\sqrt{6}-\frac{1}{8}\sqrt{15}$$

Mynegwch \frac{4\sqrt{10}}{5}\sqrt{6} fel ffracsiwn unigol.

$$\frac{4\sqrt{10}\sqrt{6}}{5}-\frac{1}{8}\sqrt{15}$$

I luosi \sqrt{10} a \sqrt{6}, dylid lluosi'r rhifau dan yr ail isradd.

$$\frac{4\sqrt{60}}{5}-\frac{1}{8}\sqrt{15}$$

Ffactora 60=2^{2}\times 15. Ailysgrifennu ail isradd y lluoswm \sqrt{2^{2}\times 15} fel lluoswm ail israddau \sqrt{2^{2}}\sqrt{15}. Cymryd isradd 2^{2}.

$$\frac{4\times 2\sqrt{15}}{5}-\frac{1}{8}\sqrt{15}$$

Lluosi 4 a 2 i gael 8.

$$\frac{8\sqrt{15}}{5}-\frac{1}{8}\sqrt{15}$$

Cyfuno \frac{8\sqrt{15}}{5} a -\frac{1}{8}\sqrt{15} i gael \frac{59}{40}\sqrt{15}.

$$\frac{59}{40}\sqrt{15}$$