Datrys (sqrt{8}-2sqrt{0.25)}-(sqrt{11/8}+sqrt{50}+2/3sqrt{12})

$$( \sqrt { 8 } - 2 \sqrt { 0.25 ) } - ( \sqrt { 1 \frac { 1 } { 8 } } + \sqrt { 50 } + \frac { 2 } { 3 } \sqrt { 12 } )$$

Enrhifo

$$-\frac{4\sqrt{3}}{3}-\frac{15\sqrt{2}}{4}-1\approx -8.612701936$$

Camau Ateb

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}.

$$2\sqrt{2}-2\sqrt{0.25}-\left(\sqrt{\frac{1\times 8+1}{8}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

Cyfrifo ail isradd 0.25 a chael 0.5.

$$2\sqrt{2}-2\times 0.5-\left(\sqrt{\frac{1\times 8+1}{8}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

Lluosi -2 a 0.5 i gael -1.

$$2\sqrt{2}-1-\left(\sqrt{\frac{1\times 8+1}{8}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

Lluosi 1 a 8 i gael 8.

$$2\sqrt{2}-1-\left(\sqrt{\frac{8+1}{8}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

Adio 8 a 1 i gael 9.

$$2\sqrt{2}-1-\left(\sqrt{\frac{9}{8}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

Ailysgrifennu ail isradd y rhaniad \sqrt{\frac{9}{8}} fel rhaniad ail israddau \frac{\sqrt{9}}{\sqrt{8}}.

$$2\sqrt{2}-1-\left(\frac{\sqrt{9}}{\sqrt{8}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

Cyfrifo ail isradd 9 a chael 3.

$$2\sqrt{2}-1-\left(\frac{3}{\sqrt{8}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

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}.

$$2\sqrt{2}-1-\left(\frac{3}{2\sqrt{2}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

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

$$2\sqrt{2}-1-\left(\frac{3\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

Sgwâr \sqrt{2} yw 2.

$$2\sqrt{2}-1-\left(\frac{3\sqrt{2}}{2\times 2}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

Lluosi 2 a 2 i gael 4.

$$2\sqrt{2}-1-\left(\frac{3\sqrt{2}}{4}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

Ffactora 50=5^{2}\times 2. Ailysgrifennu ail isradd y lluoswm \sqrt{5^{2}\times 2} fel lluoswm ail israddau \sqrt{5^{2}}\sqrt{2}. Cymryd isradd 5^{2}.

$$2\sqrt{2}-1-\left(\frac{3\sqrt{2}}{4}+5\sqrt{2}+\frac{2}{3}\sqrt{12}\right)$$

Cyfuno \frac{3\sqrt{2}}{4} a 5\sqrt{2} i gael \frac{23}{4}\sqrt{2}.

$$2\sqrt{2}-1-\left(\frac{23}{4}\sqrt{2}+\frac{2}{3}\sqrt{12}\right)$$

Ffactora 12=2^{2}\times 3. Ailysgrifennu ail isradd y lluoswm \sqrt{2^{2}\times 3} fel lluoswm ail israddau \sqrt{2^{2}}\sqrt{3}. Cymryd isradd 2^{2}.

$$2\sqrt{2}-1-\left(\frac{23}{4}\sqrt{2}+\frac{2}{3}\times 2\sqrt{3}\right)$$

Mynegwch \frac{2}{3}\times 2 fel ffracsiwn unigol.

$$2\sqrt{2}-1-\left(\frac{23}{4}\sqrt{2}+\frac{2\times 2}{3}\sqrt{3}\right)$$

Lluosi 2 a 2 i gael 4.

$$2\sqrt{2}-1-\left(\frac{23}{4}\sqrt{2}+\frac{4}{3}\sqrt{3}\right)$$

I ddod o hyd i wrthwyneb \frac{23}{4}\sqrt{2}+\frac{4}{3}\sqrt{3}, dewch o hyd i wrthwyneb pob term.

$$2\sqrt{2}-1-\frac{23}{4}\sqrt{2}-\frac{4}{3}\sqrt{3}$$

Cyfuno 2\sqrt{2} a -\frac{23}{4}\sqrt{2} i gael -\frac{15}{4}\sqrt{2}.

$$-\frac{15}{4}\sqrt{2}-1-\frac{4}{3}\sqrt{3}$$

Ffactor

$$\frac{-16 \sqrt{3} - 45 \sqrt{2} - 12}{12} = -8.61270193565761$$