Réitigh (sqrt{8}-2sqrt{025)}-(sqrt{11/8}+sqrt{50}+2/3sqrt{12})

$$( \sqrt { 8 } - 2 \sqrt { 025 ) } - ( \sqrt { 1 \frac { 1 } { 8 } } + \sqrt { 50 } + \frac { 2 } { 3 } \sqrt { 12 } )$$

Luacháil

$$-\frac{4\sqrt{3}}{3}-\frac{15\sqrt{2}}{4}-10\approx -17.612701936$$

Céimeanna Réitigh

Fachtóirigh 8=2^{2}\times 2. Athscríobh fréamh cearnach an toraidh \sqrt{2^{2}\times 2} mar thoradh na bhfréamhacha cearnacha \sqrt{2^{2}}\sqrt{2}. Tóg fréamh chearnach 2^{2}.

$$2\sqrt{2}-2\sqrt{25}-\left(\sqrt{\frac{1\times 8+1}{8}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

Áirigh fréamh chearnach 25 agus faigh 5.

$$2\sqrt{2}-2\times 5-\left(\sqrt{\frac{1\times 8+1}{8}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

Méadaigh -2 agus 5 chun -10 a fháil.

$$2\sqrt{2}-10-\left(\sqrt{\frac{1\times 8+1}{8}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

Méadaigh 1 agus 8 chun 8 a fháil.

$$2\sqrt{2}-10-\left(\sqrt{\frac{8+1}{8}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

Suimigh 8 agus 1 chun 9 a fháil.

$$2\sqrt{2}-10-\left(\sqrt{\frac{9}{8}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

Athscríobh fréamh cearnach na roinnte \sqrt{\frac{9}{8}} mar roinnt na bhfréamhacha cearnacha \frac{\sqrt{9}}{\sqrt{8}}.

$$2\sqrt{2}-10-\left(\frac{\sqrt{9}}{\sqrt{8}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

Áirigh fréamh chearnach 9 agus faigh 3.

$$2\sqrt{2}-10-\left(\frac{3}{\sqrt{8}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

Fachtóirigh 8=2^{2}\times 2. Athscríobh fréamh cearnach an toraidh \sqrt{2^{2}\times 2} mar thoradh na bhfréamhacha cearnacha \sqrt{2^{2}}\sqrt{2}. Tóg fréamh chearnach 2^{2}.

$$2\sqrt{2}-10-\left(\frac{3}{2\sqrt{2}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

Iolraigh an t-uimhreoir agus an t-ainmneoir faoi \sqrt{2} chun ainmneoir \frac{3}{2\sqrt{2}} a thiontú in uimhir chóimheasta.

$$2\sqrt{2}-10-\left(\frac{3\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

Is é 2 uimhir chearnach \sqrt{2}.

$$2\sqrt{2}-10-\left(\frac{3\sqrt{2}}{2\times 2}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

Méadaigh 2 agus 2 chun 4 a fháil.

$$2\sqrt{2}-10-\left(\frac{3\sqrt{2}}{4}+\sqrt{50}+\frac{2}{3}\sqrt{12}\right)$$

Fachtóirigh 50=5^{2}\times 2. Athscríobh fréamh cearnach an toraidh \sqrt{5^{2}\times 2} mar thoradh na bhfréamhacha cearnacha \sqrt{5^{2}}\sqrt{2}. Tóg fréamh chearnach 5^{2}.

$$2\sqrt{2}-10-\left(\frac{3\sqrt{2}}{4}+5\sqrt{2}+\frac{2}{3}\sqrt{12}\right)$$

Comhcheangail \frac{3\sqrt{2}}{4} agus 5\sqrt{2} chun \frac{23}{4}\sqrt{2} a fháil.

$$2\sqrt{2}-10-\left(\frac{23}{4}\sqrt{2}+\frac{2}{3}\sqrt{12}\right)$$

Fachtóirigh 12=2^{2}\times 3. Athscríobh fréamh cearnach an toraidh \sqrt{2^{2}\times 3} mar thoradh na bhfréamhacha cearnacha \sqrt{2^{2}}\sqrt{3}. Tóg fréamh chearnach 2^{2}.

$$2\sqrt{2}-10-\left(\frac{23}{4}\sqrt{2}+\frac{2}{3}\times 2\sqrt{3}\right)$$

Scríobh \frac{2}{3}\times 2 mar chodán aonair.

$$2\sqrt{2}-10-\left(\frac{23}{4}\sqrt{2}+\frac{2\times 2}{3}\sqrt{3}\right)$$

Méadaigh 2 agus 2 chun 4 a fháil.

$$2\sqrt{2}-10-\left(\frac{23}{4}\sqrt{2}+\frac{4}{3}\sqrt{3}\right)$$

Chun an mhalairt ar \frac{23}{4}\sqrt{2}+\frac{4}{3}\sqrt{3} a aimsiú, aimsigh an mhalairt ar gach téarma.

$$2\sqrt{2}-10-\frac{23}{4}\sqrt{2}-\frac{4}{3}\sqrt{3}$$

Comhcheangail 2\sqrt{2} agus -\frac{23}{4}\sqrt{2} chun -\frac{15}{4}\sqrt{2} a fháil.

$$-\frac{15}{4}\sqrt{2}-10-\frac{4}{3}\sqrt{3}$$

Fachtóirigh

$$\frac{-16 \sqrt{3} - 45 \sqrt{2} - 120}{12} = -17.612701935657608$$