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

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

Evaluate

$$54\sqrt{6}\approx 132.27244611$$

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}.

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

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

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

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}.

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

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

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

Multiply 6 and 9 to get 54.

$$54\sqrt{6}$$