Solve -sqrt{8}-sqrt{3}(3sqrt{6}-sqrt{24})

$$- \sqrt { 8 } - \sqrt { 3 } ( 3 \sqrt { 6 } - \sqrt { 24 } )$$

Evaluate

$$-5\sqrt{2}\approx -7.071067812$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

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

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

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

Combine 3\sqrt{6} and -2\sqrt{6} to get \sqrt{6}.

$$-2\sqrt{2}-\sqrt{3}\sqrt{6}$$

Factor 6=3\times 2. Rewrite the square root of the product \sqrt{3\times 2} as the product of square roots \sqrt{3}\sqrt{2}.

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

Multiply \sqrt{3} and \sqrt{3} to get 3.

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

Combine -2\sqrt{2} and -3\sqrt{2} to get -5\sqrt{2}.

$$-5\sqrt{2}$$