Solve sqrt{2}-sqrt{8}+2sqrt{72}

$$\sqrt{ 2 } - \sqrt{ 8 } +2 \sqrt{ 72 }$$

Evaluate

$$11\sqrt{2}\approx 15.556349186$$

Solution Steps

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}.

$$\sqrt{2}-2\sqrt{2}+2\sqrt{72}$$

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

$$-\sqrt{2}+2\sqrt{72}$$

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

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

Multiply 2 and 6 to get 12.

$$-\sqrt{2}+12\sqrt{2}$$

Combine -\sqrt{2} and 12\sqrt{2} to get 11\sqrt{2}.

$$11\sqrt{2}$$