Solve 5-sqrt{6}-sqrt{24}+5sqrt{54}-sqrt{600}

$$5 - \sqrt { 6 } - \sqrt { 24 } + 5 \sqrt { 54 } - \sqrt { 600 }$$

Evaluate

$$2\sqrt{6}+5\approx 9.898979486$$

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}.

$$5-\sqrt{6}-2\sqrt{6}+5\sqrt{54}-\sqrt{600}$$

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

$$5-3\sqrt{6}+5\sqrt{54}-\sqrt{600}$$

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}.

$$5-3\sqrt{6}+5\times 3\sqrt{6}-\sqrt{600}$$

Multiply 5 and 3 to get 15.

$$5-3\sqrt{6}+15\sqrt{6}-\sqrt{600}$$

Combine -3\sqrt{6} and 15\sqrt{6} to get 12\sqrt{6}.

$$5+12\sqrt{6}-\sqrt{600}$$

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}.

$$5+12\sqrt{6}-10\sqrt{6}$$

Combine 12\sqrt{6} and -10\sqrt{6} to get 2\sqrt{6}.

$$5+2\sqrt{6}$$