Solve sqrt{3}*(sqrt{54}-sqrt{6})=

$$\sqrt { 3 } \cdot ( \sqrt { 54 } - \sqrt { 6 } ) =$$

Evaluate

$$6\sqrt{2}\approx 8.485281374$$

Solution Steps

Factor 54=3^{2}\times 6. Rewrite the square root of the product \sqrt{3^{2}\times 6} as the product of square roots \sqrt{3^{2}}\sqrt{6}. Take the square root of 3^{2}.

$$\sqrt{3}\left(3\sqrt{6}-\sqrt{6}\right)$$

Combine 3\sqrt{6} and -\sqrt{6} to get 2\sqrt{6}.

$$\sqrt{3}\times 2\sqrt{6}$$

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

$$\sqrt{3}\times 2\sqrt{3}\sqrt{2}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$3\times 2\sqrt{2}$$

Multiply 3 and 2 to get 6.

$$6\sqrt{2}$$