Solve sqrt{6}*(sqrt{24}-sqrt{54})

$$\sqrt { 6 } \cdot ( \sqrt { 24 } - \sqrt { 54 } )$$

Evaluate

$$-6$$

Solution Steps

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

$$\sqrt{6}\left(2\sqrt{6}-\sqrt{54}\right)$$

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}.

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

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

$$\sqrt{6}\left(-1\right)\sqrt{6}$$

Multiply \sqrt{6} and \sqrt{6} to get 6.

$$6\left(-1\right)$$

Multiply 6 and -1 to get -6.

$$-6$$

Factor

$$-6$$