Lutasin ang 2sqrt{6}(sqrt{18}-24sqrt{11/3})-2sqrt{3}(sqrt{24}+4)

$$2 \sqrt { 6 } ( \sqrt { 18 } - 24 \sqrt { 1 \frac { 1 } { 3 } } ) - 2 \sqrt { 3 } ( \sqrt { 24 } + 4 )$$

I-evaluate

$$4\left(\sqrt{3}-27\sqrt{2}\right)\approx -145.806861506$$

Mga Hakbang ng Solution

I-factor out ang 18=3^{2}\times 2. I-rewrite ang square root ng product na \sqrt{3^{2}\times 2} bilang product ng mga square root na \sqrt{3^{2}}\sqrt{2}. Kunin ang square root ng 3^{2}.

$$2\sqrt{6}\left(3\sqrt{2}-24\sqrt{\frac{1\times 3+1}{3}}\right)-2\sqrt{3}\left(\sqrt{24}+4\right)$$

I-multiply ang 1 at 3 para makuha ang 3.

$$2\sqrt{6}\left(3\sqrt{2}-24\sqrt{\frac{3+1}{3}}\right)-2\sqrt{3}\left(\sqrt{24}+4\right)$$

Idagdag ang 3 at 1 para makuha ang 4.

$$2\sqrt{6}\left(3\sqrt{2}-24\sqrt{\frac{4}{3}}\right)-2\sqrt{3}\left(\sqrt{24}+4\right)$$

I-rewrite ang square root ng division na \sqrt{\frac{4}{3}} bilang division ng mga square root na \frac{\sqrt{4}}{\sqrt{3}}.

$$2\sqrt{6}\left(3\sqrt{2}-24\times \frac{\sqrt{4}}{\sqrt{3}}\right)-2\sqrt{3}\left(\sqrt{24}+4\right)$$

Kalkulahin ang square root ng 4 at makuha ang 2.

$$2\sqrt{6}\left(3\sqrt{2}-24\times \frac{2}{\sqrt{3}}\right)-2\sqrt{3}\left(\sqrt{24}+4\right)$$

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

$$2\sqrt{6}\left(3\sqrt{2}-24\times \frac{2\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\right)-2\sqrt{3}\left(\sqrt{24}+4\right)$$

Ang square ng \sqrt{3} ay 3.

$$2\sqrt{6}\left(3\sqrt{2}-24\times \frac{2\sqrt{3}}{3}\right)-2\sqrt{3}\left(\sqrt{24}+4\right)$$

Kanselahin ang greatest common factor na 3 sa 24 at 3.

$$2\sqrt{6}\left(3\sqrt{2}-8\times 2\sqrt{3}\right)-2\sqrt{3}\left(\sqrt{24}+4\right)$$

I-factor out ang 24=2^{2}\times 6. I-rewrite ang square root ng product na \sqrt{2^{2}\times 6} bilang product ng mga square root na \sqrt{2^{2}}\sqrt{6}. Kunin ang square root ng 2^{2}.

$$2\sqrt{6}\left(3\sqrt{2}-8\times 2\sqrt{3}\right)-2\sqrt{3}\left(2\sqrt{6}+4\right)$$

I-multiply ang 8 at 2 para makuha ang 16.

$$2\sqrt{6}\left(3\sqrt{2}-16\sqrt{3}\right)-2\sqrt{3}\left(2\sqrt{6}+4\right)$$

Gamitin ang distributive property para i-multiply ang 2\sqrt{6} gamit ang 3\sqrt{2}-16\sqrt{3}.

$$6\sqrt{6}\sqrt{2}-32\sqrt{3}\sqrt{6}-2\sqrt{3}\left(2\sqrt{6}+4\right)$$

I-factor out ang 6=2\times 3. I-rewrite ang square root ng product na \sqrt{2\times 3} bilang product ng mga square root na \sqrt{2}\sqrt{3}.

$$6\sqrt{2}\sqrt{3}\sqrt{2}-32\sqrt{3}\sqrt{6}-2\sqrt{3}\left(2\sqrt{6}+4\right)$$

I-multiply ang \sqrt{2} at \sqrt{2} para makuha ang 2.

$$6\times 2\sqrt{3}-32\sqrt{3}\sqrt{6}-2\sqrt{3}\left(2\sqrt{6}+4\right)$$

I-multiply ang 6 at 2 para makuha ang 12.

$$12\sqrt{3}-32\sqrt{3}\sqrt{6}-2\sqrt{3}\left(2\sqrt{6}+4\right)$$

I-factor out ang 6=3\times 2. I-rewrite ang square root ng product na \sqrt{3\times 2} bilang product ng mga square root na \sqrt{3}\sqrt{2}.

$$12\sqrt{3}-32\sqrt{3}\sqrt{3}\sqrt{2}-2\sqrt{3}\left(2\sqrt{6}+4\right)$$

I-multiply ang \sqrt{3} at \sqrt{3} para makuha ang 3.

$$12\sqrt{3}-32\times 3\sqrt{2}-2\sqrt{3}\left(2\sqrt{6}+4\right)$$

I-multiply ang -32 at 3 para makuha ang -96.

$$12\sqrt{3}-96\sqrt{2}-2\sqrt{3}\left(2\sqrt{6}+4\right)$$

Gamitin ang distributive property para i-multiply ang -2\sqrt{3} gamit ang 2\sqrt{6}+4.

$$12\sqrt{3}-96\sqrt{2}-4\sqrt{3}\sqrt{6}-8\sqrt{3}$$

I-factor out ang 6=3\times 2. I-rewrite ang square root ng product na \sqrt{3\times 2} bilang product ng mga square root na \sqrt{3}\sqrt{2}.

$$12\sqrt{3}-96\sqrt{2}-4\sqrt{3}\sqrt{3}\sqrt{2}-8\sqrt{3}$$

I-multiply ang \sqrt{3} at \sqrt{3} para makuha ang 3.

$$12\sqrt{3}-96\sqrt{2}-4\times 3\sqrt{2}-8\sqrt{3}$$

I-multiply ang -4 at 3 para makuha ang -12.

$$12\sqrt{3}-96\sqrt{2}-12\sqrt{2}-8\sqrt{3}$$

Pagsamahin ang -96\sqrt{2} at -12\sqrt{2} para makuha ang -108\sqrt{2}.

$$12\sqrt{3}-108\sqrt{2}-8\sqrt{3}$$

Pagsamahin ang 12\sqrt{3} at -8\sqrt{3} para makuha ang 4\sqrt{3}.

$$4\sqrt{3}-108\sqrt{2}$$

I-factor

$$4 {(\sqrt{3} - 27 \sqrt{2})} = -145.806861506$$