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

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

Evaluate

$$3\sqrt{3}-\sqrt{2}-27\approx -23.21806114$$

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}.

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

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

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