Solve (sqrt{600}+sqrt{6}-sqrt{24})*sqrt{6}

$$( \sqrt { 600 } + \sqrt { 6 } - \sqrt { 24 } ) \cdot \sqrt { 6 }$$

Evaluate

$$54$$

Solution Steps

Factor 600=10^{2}\times 6. Rewrite the square root of the product \sqrt{10^{2}\times 6} as the product of square roots \sqrt{10^{2}}\sqrt{6}. Take the square root of 10^{2}.

$$\left(10\sqrt{6}+\sqrt{6}-\sqrt{24}\right)\sqrt{6}$$

Combine 10\sqrt{6} and \sqrt{6} to get 11\sqrt{6}.

$$\left(11\sqrt{6}-\sqrt{24}\right)\sqrt{6}$$

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}.

$$\left(11\sqrt{6}-2\sqrt{6}\right)\sqrt{6}$$

Combine 11\sqrt{6} and -2\sqrt{6} to get 9\sqrt{6}.

$$9\sqrt{6}\sqrt{6}$$

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

$$9\times 6$$

Multiply 9 and 6 to get 54.

$$54$$

Factor

$$2\times 3^{3}$$