Solve sqrt{24}+sqrt{2}+3sqrt{6}-sqrt{8}

$$\sqrt { 24 } + \sqrt { 2 } + 3 \sqrt { 6 } - \sqrt { 8 }$$

Evaluate

$$5\sqrt{6}-\sqrt{2}\approx 10.833235152$$

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}.

$$2\sqrt{6}+\sqrt{2}+3\sqrt{6}-\sqrt{8}$$

Combine 2\sqrt{6} and 3\sqrt{6} to get 5\sqrt{6}.

$$5\sqrt{6}+\sqrt{2}-\sqrt{8}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

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

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

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