Datrys sqrt{75}*frac{sqrt{6}}{3}div1/sqrt{2}

$$\sqrt { 75 } \times \frac { \sqrt { 6 } } { 3 } \div \frac { 1 } { \sqrt { 2 } }$$

Enrhifo

$$10$$

Camau Ateb

Ffactora 75=5^{2}\times 3. Ailysgrifennu ail isradd y lluoswm \sqrt{5^{2}\times 3} fel lluoswm ail israddau \sqrt{5^{2}}\sqrt{3}. Cymryd isradd 5^{2}.

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

Mynegwch 5\times \frac{\sqrt{6}}{3} fel ffracsiwn unigol.

$$\frac{\frac{5\sqrt{6}}{3}\sqrt{3}}{\frac{1}{\sqrt{2}}}$$

Mae'n rhesymoli enwadur \frac{1}{\sqrt{2}} drwy luosi'r rhifiadur a'r enwadur â \sqrt{2}.

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

Sgwâr \sqrt{2} yw 2.

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

Mynegwch \frac{5\sqrt{6}}{3}\sqrt{3} fel ffracsiwn unigol.

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

Rhannwch \frac{5\sqrt{6}\sqrt{3}}{3} â \frac{\sqrt{2}}{2} drwy luosi \frac{5\sqrt{6}\sqrt{3}}{3} â chilydd \frac{\sqrt{2}}{2}.

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

Mae'n rhesymoli enwadur \frac{5\sqrt{6}\sqrt{3}\times 2}{3\sqrt{2}} drwy luosi'r rhifiadur a'r enwadur â \sqrt{2}.

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

Sgwâr \sqrt{2} yw 2.

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

Ffactora 6=3\times 2. Ailysgrifennu ail isradd y lluoswm \sqrt{3\times 2} fel lluoswm ail israddau \sqrt{3}\sqrt{2}.

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

Lluosi \sqrt{3} a \sqrt{3} i gael 3.

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

Lluosi 5 a 3 i gael 15.

$$\frac{15\sqrt{2}\times 2\sqrt{2}}{3\times 2}$$

Lluosi 15 a 2 i gael 30.

$$\frac{30\sqrt{2}\sqrt{2}}{3\times 2}$$

Lluosi \sqrt{2} a \sqrt{2} i gael 2.

$$\frac{30\times 2}{3\times 2}$$

Lluosi 30 a 2 i gael 60.

$$\frac{60}{3\times 2}$$

Lluosi 3 a 2 i gael 6.

$$\frac{60}{6}$$

Rhannu 60 â 6 i gael 10.

$$10$$

Ffactor

$$2\times 5$$