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

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

I-evaluate

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

Mga Hakbang ng Solution

I-factor out ang 8=2^{2}\times 2. I-rewrite ang square root ng product na \sqrt{2^{2}\times 2} bilang product ng mga square root na \sqrt{2^{2}}\sqrt{2}. Kunin ang square root ng 2^{2}.

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

Kalkulahin ang square root ng 25 at makuha ang 5.

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

I-multiply ang -2 at 5 para makuha ang -10.

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

I-multiply ang 1 at 8 para makuha ang 8.

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

Idagdag ang 8 at 1 para makuha ang 9.

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

I-rewrite ang square root ng division na \sqrt{\frac{9}{8}} bilang division ng mga square root na \frac{\sqrt{9}}{\sqrt{8}}.

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

Kalkulahin ang square root ng 9 at makuha ang 3.

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

I-factor out ang 8=2^{2}\times 2. I-rewrite ang square root ng product na \sqrt{2^{2}\times 2} bilang product ng mga square root na \sqrt{2^{2}}\sqrt{2}. Kunin ang square root ng 2^{2}.

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

I-rationalize ang denominator ng \frac{3}{2\sqrt{2}} sa pamamagitan ng pag-multiply ng numerator at denominator sa \sqrt{2}.

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

Ang square ng \sqrt{2} ay 2.

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

I-multiply ang 2 at 2 para makuha ang 4.

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

I-factor out ang 50=5^{2}\times 2. I-rewrite ang square root ng product na \sqrt{5^{2}\times 2} bilang product ng mga square root na \sqrt{5^{2}}\sqrt{2}. Kunin ang square root ng 5^{2}.

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

Pagsamahin ang \frac{3\sqrt{2}}{4} at 5\sqrt{2} para makuha ang \frac{23}{4}\sqrt{2}.

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

I-factor out ang 12=2^{2}\times 3. I-rewrite ang square root ng product na \sqrt{2^{2}\times 3} bilang product ng mga square root na \sqrt{2^{2}}\sqrt{3}. Kunin ang square root ng 2^{2}.

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

Ipakita ang \frac{2}{3}\times 2 bilang isang single fraction.

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

I-multiply ang 2 at 2 para makuha ang 4.

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

Para hanapin ang kabaligtaran ng \frac{23}{4}\sqrt{2}+\frac{4}{3}\sqrt{3}, hanapin ang kabaligtaran ng bawat term.

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

Pagsamahin ang 2\sqrt{2} at -\frac{23}{4}\sqrt{2} para makuha ang -\frac{15}{4}\sqrt{2}.

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

I-factor

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