Solve -2sqrt{5}-2sqrt{12}-sqrt{24}-2sqrt{3}

$$- 2 \sqrt { 5 } - 2 \sqrt { 12 } - \sqrt { 24 } - 2 \sqrt { 3 }$$

Evaluate

$$-2\sqrt{5}-2\sqrt{6}-6\sqrt{3}\approx -19.763420286$$

Solution Steps

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$-2\sqrt{5}-2\times 2\sqrt{3}-\sqrt{24}-2\sqrt{3}$$

Multiply -2 and 2 to get -4.

$$-2\sqrt{5}-4\sqrt{3}-\sqrt{24}-2\sqrt{3}$$

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}.

$$-2\sqrt{5}-4\sqrt{3}-2\sqrt{6}-2\sqrt{3}$$

Combine -4\sqrt{3} and -2\sqrt{3} to get -6\sqrt{3}.

$$-2\sqrt{5}-6\sqrt{3}-2\sqrt{6}$$