Solve sqrt{3}-sqrt{8}+sqrt{2}-sqrt{27}

$$\sqrt { 3 } - \sqrt { 8 } + \sqrt { 2 } - \sqrt { 27 }$$

Evaluate

$$-\sqrt{2}-2\sqrt{3}\approx -4.878315178$$

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}.

$$\sqrt{3}-2\sqrt{2}+\sqrt{2}-\sqrt{27}$$

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

$$\sqrt{3}-\sqrt{2}-\sqrt{27}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

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

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

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