Solve 2sqrt{128}+5sqrt{200}

$$2 \sqrt{ 128 } +5 \sqrt{ 200 }$$

Evaluate

$$66\sqrt{2}\approx 93.338095117$$

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}.

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

Multiply 2 and 8 to get 16.

$$16\sqrt{2}+5\sqrt{200}$$

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}.

$$16\sqrt{2}+5\times 10\sqrt{2}$$

Multiply 5 and 10 to get 50.

$$16\sqrt{2}+50\sqrt{2}$$

Combine 16\sqrt{2} and 50\sqrt{2} to get 66\sqrt{2}.

$$66\sqrt{2}$$