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

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

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}.

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

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

$$\sqrt{6}\sqrt{6}$$

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

$$6$$

Factor

$$2\times 3$$