Solve 2sqrt{200}+3sqrt{50}-4sqrt{8}

$$2 \sqrt { 200 } + 3 \sqrt { 50 } - 4 \sqrt { 8 }$$

Evaluate

$$27\sqrt{2}\approx 38.183766184$$

Solution Steps

Factor 200=10^{2}\times 2. Rewrite the square root of the product \sqrt{10^{2}\times 2} as the product of square roots \sqrt{10^{2}}\sqrt{2}. Take the square root of 10^{2}.

$$2\times 10\sqrt{2}+3\sqrt{50}-4\sqrt{8}$$

Multiply 2 and 10 to get 20.

$$20\sqrt{2}+3\sqrt{50}-4\sqrt{8}$$

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}.

$$20\sqrt{2}+3\times 5\sqrt{2}-4\sqrt{8}$$

Multiply 3 and 5 to get 15.

$$20\sqrt{2}+15\sqrt{2}-4\sqrt{8}$$

Combine 20\sqrt{2} and 15\sqrt{2} to get 35\sqrt{2}.

$$35\sqrt{2}-4\sqrt{8}$$

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}.

$$35\sqrt{2}-4\times 2\sqrt{2}$$

Multiply -4 and 2 to get -8.

$$35\sqrt{2}-8\sqrt{2}$$

Combine 35\sqrt{2} and -8\sqrt{2} to get 27\sqrt{2}.

$$27\sqrt{2}$$