Solve 4sqrt{8}-10sqrt{50}+10sqrt{200}

$$4 \sqrt{ 8 } -10 \sqrt{ 50 } +10 \sqrt{ 200 }$$

Evaluate

$$58\sqrt{2}\approx 82.024386618$$

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}.

$$4\times 2\sqrt{2}-10\sqrt{50}+10\sqrt{200}$$

Multiply 4 and 2 to get 8.

$$8\sqrt{2}-10\sqrt{50}+10\sqrt{200}$$

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}.

$$8\sqrt{2}-10\times 5\sqrt{2}+10\sqrt{200}$$

Multiply -10 and 5 to get -50.

$$8\sqrt{2}-50\sqrt{2}+10\sqrt{200}$$

Combine 8\sqrt{2} and -50\sqrt{2} to get -42\sqrt{2}.

$$-42\sqrt{2}+10\sqrt{200}$$

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}.

$$-42\sqrt{2}+10\times 10\sqrt{2}$$

Multiply 10 and 10 to get 100.

$$-42\sqrt{2}+100\sqrt{2}$$

Combine -42\sqrt{2} and 100\sqrt{2} to get 58\sqrt{2}.

$$58\sqrt{2}$$