Datrys -5sqrt{8/27}*sqrt{11/4}*(-3sqrt{54})

$$- 5 \sqrt { \frac { 8 } { 27 } } \times \sqrt { 1 \frac { 1 } { 4 } } \times ( - 3 \sqrt { 54 } )$$

Enrhifo

$$30\sqrt{5}\approx 67.082039325$$

Camau Ateb

Ailysgrifennu ail isradd y rhaniad \sqrt{\frac{8}{27}} fel rhaniad ail israddau \frac{\sqrt{8}}{\sqrt{27}}.

$$-5\times \frac{\sqrt{8}}{\sqrt{27}}\sqrt{\frac{4+1}{4}}\left(-3\right)\sqrt{54}$$

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}.

$$-5\times \frac{2\sqrt{2}}{\sqrt{27}}\sqrt{\frac{4+1}{4}}\left(-3\right)\sqrt{54}$$

Ffactora 27=3^{2}\times 3. Ailysgrifennu ail isradd y lluoswm \sqrt{3^{2}\times 3} fel lluoswm ail israddau \sqrt{3^{2}}\sqrt{3}. Cymryd isradd 3^{2}.

$$-5\times \frac{2\sqrt{2}}{3\sqrt{3}}\sqrt{\frac{4+1}{4}}\left(-3\right)\sqrt{54}$$

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

$$-5\times \frac{2\sqrt{2}\sqrt{3}}{3\left(\sqrt{3}\right)^{2}}\sqrt{\frac{4+1}{4}}\left(-3\right)\sqrt{54}$$

Sgwâr \sqrt{3} yw 3.

$$-5\times \frac{2\sqrt{2}\sqrt{3}}{3\times 3}\sqrt{\frac{4+1}{4}}\left(-3\right)\sqrt{54}$$

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

$$-5\times \frac{2\sqrt{6}}{3\times 3}\sqrt{\frac{4+1}{4}}\left(-3\right)\sqrt{54}$$

Lluosi 3 a 3 i gael 9.

$$-5\times \frac{2\sqrt{6}}{9}\sqrt{\frac{4+1}{4}}\left(-3\right)\sqrt{54}$$

Adio 4 a 1 i gael 5.

$$-5\times \frac{2\sqrt{6}}{9}\sqrt{\frac{5}{4}}\left(-3\right)\sqrt{54}$$

Ailysgrifennu ail isradd y rhaniad \sqrt{\frac{5}{4}} fel rhaniad ail israddau \frac{\sqrt{5}}{\sqrt{4}}.

$$-5\times \frac{2\sqrt{6}}{9}\times \frac{\sqrt{5}}{\sqrt{4}}\left(-3\right)\sqrt{54}$$

Cyfrifo ail isradd 4 a chael 2.

$$-5\times \frac{2\sqrt{6}}{9}\times \frac{\sqrt{5}}{2}\left(-3\right)\sqrt{54}$$

Lluosi -5 a -3 i gael 15.

$$15\times \frac{2\sqrt{6}}{9}\times \frac{\sqrt{5}}{2}\sqrt{54}$$

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}.

$$15\times \frac{2\sqrt{6}}{9}\times \frac{\sqrt{5}}{2}\times 3\sqrt{6}$$

Lluosi 15 a 3 i gael 45.

$$45\times \frac{2\sqrt{6}}{9}\times \frac{\sqrt{5}}{2}\sqrt{6}$$

Diddymwch y ffactor cyffredin mwyaf 9 yn 45 a 9.

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

Mynegwch 5\times 2\sqrt{6}\times \frac{\sqrt{5}}{2} fel ffracsiwn unigol.

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

Canslo 2 a 2.

$$5\sqrt{6}\sqrt{5}\sqrt{6}$$

Lluosi \sqrt{6} a \sqrt{6} i gael 6.

$$5\times 6\sqrt{5}$$

Lluosi 5 a 6 i gael 30.

$$30\sqrt{5}$$