Datrys 5sqrt{11/3}3sqrt{54}

$$5 \sqrt{ 1 \frac{ 1 }{ 3 } } 3 \sqrt{ 54 }$$

Enrhifo

$$90\sqrt{2}\approx 127.279220614$$

Camau Ateb

Lluosi 3 a 5 i gael 15.

$$15\sqrt{\frac{1\times 3+1}{3}}\sqrt{54}$$

Lluosi 1 a 3 i gael 3.

$$15\sqrt{\frac{3+1}{3}}\sqrt{54}$$

Adio 3 a 1 i gael 4.

$$15\sqrt{\frac{4}{3}}\sqrt{54}$$

Ailysgrifennu ail isradd y rhaniad \sqrt{\frac{4}{3}} fel rhaniad ail israddau \frac{\sqrt{4}}{\sqrt{3}}.

$$15\times \frac{\sqrt{4}}{\sqrt{3}}\sqrt{54}$$

Cyfrifo ail isradd 4 a chael 2.

$$15\times \frac{2}{\sqrt{3}}\sqrt{54}$$

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

$$15\times \frac{2\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\sqrt{54}$$

Sgwâr \sqrt{3} yw 3.

$$15\times \frac{2\sqrt{3}}{3}\sqrt{54}$$

Ffactora 54=3^{2}\times 6. Ailysgrifennu ail isradd y lluoswm \sqrt{3^{2}\times 6} fel lluoswm ail israddau \sqrt{3^{2}}\sqrt{6}. Cymryd isradd 3^{2}.

$$15\times \frac{2\sqrt{3}}{3}\times 3\sqrt{6}$$

Lluosi 15 a 3 i gael 45.

$$45\times \frac{2\sqrt{3}}{3}\sqrt{6}$$

Diddymwch y ffactor cyffredin mwyaf 3 yn 45 a 3.

$$15\times 2\sqrt{3}\sqrt{6}$$

Lluosi 15 a 2 i gael 30.

$$30\sqrt{3}\sqrt{6}$$

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

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

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

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

Lluosi 30 a 3 i gael 90.

$$90\sqrt{2}$$