Solve -sqrt{8}-sqrt{12}+sqrt{18}

$$- \sqrt { 8 } - \sqrt { 12 } + \sqrt { 18 }$$

Evaluate

$$\sqrt{2}-2\sqrt{3}\approx -2.049888053$$

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}.

$$-2\sqrt{2}-\sqrt{12}+\sqrt{18}$$

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}.

$$-2\sqrt{2}-2\sqrt{3}+\sqrt{18}$$

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}.

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

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

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