Solve 4sqrt{50}-sqrt{72}+2sqrt{2}

$$4 \sqrt { 50 } - \sqrt { 72 } + 2 \sqrt { 2 }$$

Evaluate

$$16\sqrt{2}\approx 22.627416998$$

Solution Steps

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$4\times 5\sqrt{2}-\sqrt{72}+2\sqrt{2}$$

Multiply 4 and 5 to get 20.

$$20\sqrt{2}-\sqrt{72}+2\sqrt{2}$$

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}.

$$20\sqrt{2}-6\sqrt{2}+2\sqrt{2}$$

Combine 20\sqrt{2} and -6\sqrt{2} to get 14\sqrt{2}.

$$14\sqrt{2}+2\sqrt{2}$$

Combine 14\sqrt{2} and 2\sqrt{2} to get 16\sqrt{2}.

$$16\sqrt{2}$$