Solve {l}{sqrt{2}-sqrt{27}}{+frac{sqrt{3}}{4}}

$$\left. \begin{array} { l } { \sqrt { 2 } - \sqrt { 27 } } \\ { + \frac { \sqrt { 3 } } { 4 } } \end{array} \right.$$

Evaluate

$$-\frac{11\sqrt{3}}{4}+\sqrt{2}\approx -3.348926158$$

Solution Steps

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}.

$$\sqrt{2}-3\sqrt{3}+\frac{\sqrt{3}}{4}$$

Combine -3\sqrt{3} and \frac{\sqrt{3}}{4} to get -\frac{11}{4}\sqrt{3}.

$$\sqrt{2}-\frac{11}{4}\sqrt{3}$$

Factor

$$\frac{4 \sqrt{2} - 11 \sqrt{3}}{4} = -3.3489261584413175$$