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

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

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}.

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

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

$$\sqrt{3}\left(-2\right)\sqrt{6}$$

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}.

$$\sqrt{3}\left(-2\right)\sqrt{3}\sqrt{2}$$

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

$$3\left(-2\right)\sqrt{2}$$

Multiply 3 and -2 to get -6.

$$-6\sqrt{2}$$