Solve 2sqrt{18}-sqrt{24}-3sqrt{8}

$$2 \sqrt { 18 } - \sqrt { 24 } - 3 \sqrt { 8 }$$

Evaluate

$$-2\sqrt{6}\approx -4.898979486$$

Solution Steps

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$2\times 3\sqrt{2}-\sqrt{24}-3\sqrt{8}$$

Multiply 2 and 3 to get 6.

$$6\sqrt{2}-\sqrt{24}-3\sqrt{8}$$

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}.

$$6\sqrt{2}-2\sqrt{6}-3\sqrt{8}$$

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}.

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

Multiply -3 and 2 to get -6.

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

Combine 6\sqrt{2} and -6\sqrt{2} to get 0.

$$-2\sqrt{6}$$