Solve sqrt{128}-2sqrt{50}+4sqrt{2}

$$\sqrt{ 128 } -2 \sqrt{ 50 } +4 \sqrt{ 2 }$$

Evaluate

$$2\sqrt{2}\approx 2.828427125$$

Solution Steps

Factor 128=8^{2}\times 2. Rewrite the square root of the product \sqrt{8^{2}\times 2} as the product of square roots \sqrt{8^{2}}\sqrt{2}. Take the square root of 8^{2}.

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

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}.

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

Multiply -2 and 5 to get -10.

$$8\sqrt{2}-10\sqrt{2}+4\sqrt{2}$$

Combine 8\sqrt{2} and -10\sqrt{2} to get -2\sqrt{2}.

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

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

$$2\sqrt{2}$$