Solve sqrt{2}*sqrt{6}-frac{sqrt{27}}{3}

$$\sqrt { 2 } \times \sqrt { 6 } - \frac { \sqrt { 27 } } { 3 }$$

Evaluate

$$\sqrt{3}\approx 1.732050808$$

Solution Steps

Factor 6=2\times 3. Rewrite the square root of the product \sqrt{2\times 3} as the product of square roots \sqrt{2}\sqrt{3}.

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

Multiply \sqrt{2} and \sqrt{2} to get 2.

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

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}.

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

Cancel out 3 and 3.

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

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

$$\sqrt{3}$$