Solve 2sqrt{50}+3sqrt{128}

$$2 \sqrt { 50 } + 3 \sqrt { 128 }$$

Evaluate

$$34\sqrt{2}\approx 48.083261121$$

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}.

$$2\times 5\sqrt{2}+3\sqrt{128}$$

Multiply 2 and 5 to get 10.

$$10\sqrt{2}+3\sqrt{128}$$

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}.

$$10\sqrt{2}+3\times 8\sqrt{2}$$

Multiply 3 and 8 to get 24.

$$10\sqrt{2}+24\sqrt{2}$$

Combine 10\sqrt{2} and 24\sqrt{2} to get 34\sqrt{2}.

$$34\sqrt{2}$$