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

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

Evaluate

$$-3\sqrt{2}\approx -4.242640687$$

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}.

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

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

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

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}.

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

Combine 3\sqrt{3} and -3\sqrt{3} to get 0.

$$-3\sqrt{2}$$