Solve 2sqrt{72}+2sqrt{2}-4sqrt{2}

$$2 \sqrt{ 72 } +2 \sqrt{ 2 } -4 \sqrt{ 2 }$$

Evaluate

$$10\sqrt{2}\approx 14.142135624$$

Solution Steps

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}.

$$2\times 6\sqrt{2}+2\sqrt{2}-4\sqrt{2}$$

Multiply 2 and 6 to get 12.

$$12\sqrt{2}+2\sqrt{2}-4\sqrt{2}$$

Combine 12\sqrt{2} and 2\sqrt{2} to get 14\sqrt{2}.

$$14\sqrt{2}-4\sqrt{2}$$

Combine 14\sqrt{2} and -4\sqrt{2} to get 10\sqrt{2}.

$$10\sqrt{2}$$